These are just my guesses, but...

1) I'd imagine that even though the Primals will be roaming with the addition of Free Companies, summoning them, etc. we'll still be able to fight them in their current form seeing as how they're tied into the Relic weapon quest. Can't comment on drops though, they still haven't told us.

2) I would guess not, as that wouldn't really be fair to new players, nor does it make sense from a design standpoint. They said they're working on making them viewable on your Lodestone history, so that'll probably be all we get.

3) Again, tied to Relic quest, and as Elexia said, Yoshi-P has said in the past that they'll all be in 2.0.

4) Yes, for sure.

5) No way of knowing, and as Elexia said, leves are going through another reform, so we'll have to wait and see.

6) Seeing as how it's tied to the Seventh Umbral Era, they'll probably be removed, but that would be a shame. Maybe they'll just change the context of the battles instead.