[If you had the chance to remake FE4 what would you add or want to see?]

Other than modest rebalancing a remake should be faithful to the original. They could add in content that was supposed to be in FE4 that was chopped out (mixed gen 1 and gen 2 teams, I believe, or at least some still-living parents in gen 2 other than Lewin). Or a "dream team" postgame campaign or something where you just pick what you like out of gen 1, gen 2 and the replacements, whatever works. SoV without the endgame is very close to the NES game other than adding Faye and more "town stuff".

 - Make certain events less luck-based (particularly Ayra's recruitment and Lachesis talking to her brother, both of which can require reloads far too often until you get good RNG)

 - Make certain characters better (Adan, Deu, Diadora and Azel are all pretty terrible, Lester and Diarmud are often bad, lategame Fynn is kind of bad due to being lance-locked, having gen 1 stats and the pegasus being a better candidate for the hero lance).

 - Remove the arena grind, find another way for characters to get money. On that note rework the money system, since it very heavily rewards top tier characters while leaving the bad characters behind, since almost every good item is an enemy drop, and the good characters like Sigurd quickly hit the 50k cap.

 - Maybe just add more spells instead of nerfing wind and buffing fire, since at the end of the day, it's really only Azel that sucks because of being stuck with fire. Lex is top tier due to elite and the hero axe, and Johan/Johavier will have Lex's Hero Axe soon after recruitment. They could slightly buff lances, I suppose. And buff the weaker classes like social knight (though its more like Noish and Alec are on the weak side as your two paladins in gen 2 are both perfectly find).

 - Add a "move all" command or a way to macro-move your army.

 - I don't see a need for an avatar. SoV didn't have one. They could add a couple new characters if they really wanted to but I really like how you have full deployment.

 - I suppose it would be nice if you got the use of siege tomes. 

 - I suppose it would be nice if the substitutes had a presence in a game where you don't kill off all of the women in gen 1. I generally kill off Sylvia since Charlot gets his berserk staff and it doesn't matter that Laylea's stats are kind of bad. All dancers are bad even if Sylvia marries Holin or Lex.

 - Modest rebalancing is likely called for as some gen 1 characters are pretty bad without loads of babying. Also its a bit silly that any unpromoted horseman (and Adan) cannot participate in the last bit of chapter 4 due to movement restrictions.

 - Have Diadora be actually good for the few chapters you actually have her.

 - Let mounted characters use sword skills.

 - FE loves its reclassing and I guess that might give you a way to customize your army but its not really necessary.
 

[What are some fun FE4 challenge runs?]

Adan is the father of every child unit.

[Fire Emblem 4 Randomizer]

Hey so I played through to around chapter 9. Possibly my fault for choosing bad settings, but there were a lot of characters in the 1st generation that had complete garbage growths. 

Chapter 6 was hilarious. Celice was a priest. Mana was a priest. Rodney was... a priest. And Rondalvan was a thief with the kind of level 1 garbage stats that Dew starts with.

Tristan was a dragon knight and Dimna was an axe figther. And Oifaye is was a mage knight who can promote to paladin at level 20 even though i said, promot only to same weapon use classes.

Celice later promoted to master knight so thumbsup for that.

 

Problem: Sety starts with a Duke Knight sprite on the map, garbled dots in the status screen. Zero movement and the game freezes if you attack with him. Major Tordo and Hezul (makes sense considering his parents). And he can use C staffs, B fire, garbled sprite thunder,  A wind, garbled sprite light and and C dark.  Probably just garbage data with the randomizer selecting a class outside the range in the ROM?

 

Not complaining but its funny how I got so many flyers and priests in this one. And three axe knights in generation 1. The game is a lot harder with barely any mounted units and having barely any melee units in chapter 6 and 7. Also a lot of melee units had very low HP. Like, less than 30 at level 10, so the game played more like Fates where you can't just tank entire armies.