Well, I know several people have responded already, and you've gotten lots of input by this point, but since I got a notification and had already written too much, I'm just going ahead with this post. I run Y!Tiki/Nowi/Ninian on my main offensive team, and out of pride I pretty much run nothing but them in all of my Arena / Grand Hero battles. So I'll try to respond to your question about Young Tiki. Most of what I'll say below is mostly based off of personal experience, rather than any hard calculations (Since so many other people do that here, I don't really feel the need to go out of my way to do the same) although I do include a few vague match-ups with potential Julia and Lucina because they're important enough. Hopefully they might provide even a bit more insight, since you've gotten so much of it already from other people.
Young Tiki is indeed a very solid unit, and I certainly recommend using her if you can. I myself use her in my main team and I can definitely say that she's very good at tanking a multitude of units while still dishing out heavy damage in return. In addition, her high base stat totals will land you better Arena scores in general, although it will also make you more likely to be paired up against merged units. She's strong enough that she can deal respectable damage against Blue(s) and even tank them relatively often, although obviously you don't want to push it too much. Here a few recommendations for what I think might be worth considering, although which ones are best for you really depends on your specific situation, some of which I factored in the explanations.
Like many others would tell you, Lightning Breath+ is pretty much a given here. Trading -4 Atk in exchange for being able to counter at any range is very useful, and will land you far more defense wins in general. That being said however, one thing to keep in mind is that you'll be doing a whole lot of grinding just to give her this one weapon. To demonstrate, you need 300 SP for Lightning Breath and then another 450 SP for Lightning Breath+, for a total of 750 SP altogether. Unless you're a whale and can afford to merge several of her together, you will be needing to put lots of time into her to not only give her this weapon but her other skills as well. I have been hard-grinding her almost daily ever since Skill Inheritance was finally implemented, and I can tell you that it requires dedication. The end result will be worth it though, as you get the equivalent of a tanky Takumi.
It's worth noting though, that her default Flametongue+ is a fine weapon too. Having +4 Atk can help secure a lot of kills, and when you're using her offensively, you won't find yourself desperately wishing for that extra range too often. The lack of Green Mages besides Julia and Nino kind of softens the blow on not being able to counter at any range, so it's not completely unfeasible to simply stick to her default weapon if you don't have time. In addition, Flametongue+ can secure ORKOs against merged Julia(s), which Lightning Breath+ will start failing to do after a while.
Her A-Passive really depends on what your team composition is like. If you happen to be using a full-manakete team, or you don't have other units that can reliably take out Julia, then you'd most likely want to consider Triangle Adept. It'll really soften the blow on Y!Tiki, and will reduce her damage taken by approximately 15 whenever she's struck. It will also give Y!Tiki enough power to 2HKO most Julia(s) in return, which is something you'd want to take into consideration when thinking about the B-Passive. Although if you're using a manakete in your team, there's also a fair chance you'll run into merged Julia(s) that are tanky enough to take 2 hits from a Triangle Adept Y!Tiki, so there's that to consider as well. In general this is the skill to take if you absolutely don't have anyone else to answer to Julia.
However, I generally don't recommend Triangle Adept if you aren't going full-manakete. Honestly speaking, you rather avoid having Y!Tiki face off against Julia or Falchion-wielders if you can help it at all. You aren't even guaranteed to ORKO (with Lightning Breath+) Julia if you revolve your whole build around that sole purpose, so I generally don't see it as worth all the time and effort. In addition, Y!Tiki is strong enough that she can consistently take hits from Blue units and even return significant damage to them. If you run Triangle Adept, you'll kind of ruin her ability to do all that, in exchange for being better equipped to deal with a single threat that might not even show up all that often. She will almost never have trouble with green units besides Julia and maaaaaybe a fat Nino, so the payout isn't that much. As such, there are a variety of other options which you can consider:
Fury 3, as suggested by @MaskedAmpharos is one fine solution. If your Y!Tiki isn't doesn't have a +Spd boon, it will save you from being doubled by a notable number of units. However, it's a double-edged blade, because Y!Tiki is capable of taking a lot of non-Blue hits, and having it equipped might kill her faster in the long run. I would generally recommend it if your Y!Tiki isn't +Spd, as not being doubled will usually save you more damage than Fury is dealing to you, but if she is, she's fast enough not to be doubled by a lot of units and you might want to start considering other options instead. If you have a healer though, the viability of this skill will shoot way up, and I'd definitely recommend it regardless of what kind of Y!Tiki you happened to roll. Having someone to consistently heal her would make Fury 3 probably one of the best possible skills on her.
Not many people like them, but I personally find the Defiant series of skills to be quite useful on the manaketes. +7 boost to a particular stat is huge, and most manaketes such as Y!Tiki are tanky enough that they'll fall into Defiant range before they are ever killed. Since you'll mostly likely be using Y!Tiki as a tank, and she will very often be tanking several hits a turn due to that fact, slapping a Defiant Def/Res onto her can save her from being killed in several situations. Especially Defiant Def, which can very likely turn the damage Y!Tiki receives from most Axe-users and certain Sword-users to a pretty-looking 0. I wouldn't strongly recommend these though; they are just something worth keeping in mind. Unless you happen to be running Vantage, at which point I really do enjoy Defiant Atk on Y!Tiki because of how funny it can become. (I'll elaborate on that later)
Honestly speaking, Y!Tiki's default Armored Blow isn't that bad either. It grants you +6 Def when initiating an attack, which is honestly all kinds of amazing. It can make you take a whopping 0 damage from Hector when initiating on him, and likewise for many other axe-users in the game. It will also allow her to initiate on blue units and come out with more than half her heath intact relatively often, which is nice when you need to do some chip damage so someone else can go in for the kill. It's good enough that I would have it as one of the later skills to replace. At the very least, having tried both Fury 3 and Armored Blow out, it does feel like Armored Blow keeps my Y!Tiki alive longer than Fury 3 in the long run. Although obviously, this is less true when you're up against nothing but mages.
I know people have recommended Swordbreaker, but I'm not very fond of it honestly. Mostly because Chrom and Lucina have a very good chance of simply one-shotting Y!Tiki, and it's very possible that Swordbreaker won't get a chance to come into play at all. Lucina especially becomes disgustingly common in the higher up tiers, and you'll reach a point where you see nothing but 40+10 Lucina(s) that are likely to skewer Y!Tiki. I would keep Y!Tiki away from Falchion(s) if at all possible, even more so than Julia's Naga, just because of how dangerous they are to her. If you must use a dragon to deal with them, use Nowi seriously. Nowi has a good chance of one-shotting Falchion-users and is generally a much more pretty-looking match-up. Although the best scenario is simply using some Lance-user with decent Def.
Green Tomebreaker is definitely worth considering if you're already running Triangle Adept. in fact, it's worth considering even if you aren't. It'll either deal heavy damage to Julia or outright ORKO her, depending on your build and what Julia you're facing. In any case though, it'll make finishing her off a whole lot easier for someone else on your team, and it's a very safe tactic unless your opponent decided to sacrifice their Takumi to Julia for some reason.
I feel like one of the best B-Passives though, is definitely Renewal. Y!Tiki is definitely tanky enough to last several hits, so Renewal can go a long way in healing her up throughout the match. In fact, if you have movement assists on your team, it becomes even more useful as Y!Tiki can simply start kiting the opponent to heal up to full health unopposed, and can later enter back into the fight with a capped health bar. It's also a great complement to Fury 3, as it gives you a chance to rest off some of the damage that Fury 3 has been dealing to you over time. And finally, it's great if you're not running a healer as you have at least one consistent method of self-healing.
As some have suggested, Quick Riposte is also a fine choice. It'll help you get some heavy early damage in, around the time where you can still pick out specific enemies for Y!Tiki to face off against. She's tanky enough that you have a small but existing chance to proc it twice, and if you do have a healer, this skill becomes downright amazing. You can just keep healing Y!Tiki back to full health, which is not hard to do with something like Rehabilitate, and Y!Tiki can keep proccing the skill over and over while maintaining a bulk that's unlikely to have her ORKO'd by anyone not wielding a Falchion or Naga. It's a must-have if you're running a healer, although if you aren't, it's still something worth considering.
The Seal skills are something worth considering as well. They don't shine too much in a 1v1 environment, but their real worth will come out when a tank is equipping them in a team-based battle. Since Y!Tiki is likely to be one of your main tanks, and will be sponging a number of hits, that also means she will have the opportunity to hand out a great number of debuffs if you're willing to slap a Seal skill on her. For example, giving her Seal Spd means that if 2-3 opponents are attacking her, when your turn comes, pretty much absolutely everyone on your team can double all of those units. -7 to a particular stat is such a huge handicap that your team as a whole will love Y!Tiki to death for debuffing the enemy team so hard. It's not particularly useful if you're relying on Y!Tiki to handle everything, but it can be very good depending on how offensive and mobile your team is.
Finally, I am a big personal fan of Vantage on units that can counter at any range. It annoys me to no end when I have to face it, and I know my +10 defense wins on the first day of the season was probably annoyed by it too (I run Y!Tiki/Nowi/Ryoma/Takumi all on Defiant Atk+Vantage). A very popular tactic for a lot of people is the 'bait on enemy phase and kill on player phase' strategy, but Vantage kind of screws with that hard. In addition, on units that can counter at any range, it pretty much ensures that your opponent has absolutely no choice but to take at least one hard hit to the face before finally finishing your unit. As such it's an excellent skill for defense teams, and it can be very useful if you know what you're doing on offensive runs too. If some enemy unit is 1 hit away from death, having Vantage basically means you can proceed to ignore them completely and not waste a turn because they can neither do anything to survive nor deal any further damage to you. You can simply have your Y!Tiki move on to some other unit that needs killing or at least some damage chipping in. >75% Hp is honestly a very generous activation requirement that you're going to hit before ever dying with her. It can be rather situational though, so some of the above skills might work out more consistently for you. If you do run Vantage, you might want to consider running Defiant Atk 3 as well, simply so that your Y!Tiki has +7 Atk when in this range, ensuring that she hits back extra hard and it will also make her hurt significantly more.
If you're running a Manakete Team and you're super-lucky, give her Fortify Dragons. Otherwise, literally any Hone or Spur would work pretty well here. I don't think there's any universal answer for which stat to buff is the best, and it really depends on what your team needs. I have Spur Atk 3 simply because it ensures that my Nowi can cleanly OHKO opposing Lucina(s) and Marth(s), but your team might have use for Spd or something. Alternatively, if your team doesn't need any help whatsoever, Threaten Atk/Spd or Threaten Res can work on her as well, as it will help her to either tank melee units or kill them. Both of which is lovely. I generally would stay away from Breath of Life unless you're using a Dancer or something, because the positioning it requires is just so situational that it's often not worth the skill slot.
Like the above, any Rally that your team needs you can be thrown in here. Otherwise, get a movement assist. Draw Back, Reposition, Smite and Swap are all excellent choices if you know what you're doing with them and if you think your team needs them. Personally speaking, I'd say Reposition and Swap are preferable if you run at least one assassin unit that's super good at killing but is extremely unlikely to survive being attacked. It'll allow them to run ahead of Y!Tiki, kill some schmuck, then get shoved behind her so she can protect that unit. Smite is really good for pushing units toward a certain direction, if you happen to need someone far away killed (Or you're surrounded by cavalry and need to save someone). Draw Back is usually good for ranged units, and it might be hard for Y!Tiki to use since she's usually on the front lines, so unless you have some strategy in mind for it, I wouldn't recommend it as much as the others.
It really doesn't matter what you throw in here, but I do like Bonfire since the manaketes have high Def. You can throw in any similar skill here though, they won't make too much of a difference.