There may be slight differences. For Priests, at least, I suspect they'll share Clerics' +5 healing skill, but replace Miracle with something else. There may also be slight statistical differences, but probably nothing huge. Priests, for example, may have a slightly lower Res base stat so they won't have a negative promotion gain when promoting to Sage.
Priest->BattleMonk is probably the same thing just, well, not "sister".
Adoption wouldn't explain inherited physical traits.
They could adopt!! For Nagi's sake, there have been orphanages throught out the FE history, with Lucius being the Father of one (or implied to be) in FE6.
As much as I'd love to produce Sylvia the Master Sniper through lesbian sex with Serge, I don't think it's happening.