1. You do, for the most part, mash A. The strategy comes from setup, especially later on. But it never evolves beyond that really.
2. Yep.
3. Normal.
4. Make sure you have dash (which you clearly have done) to open rooms in an early dungeon, otherwise focus on stuff that aids in combat. For the weirder out of battle skills, only one person in your party needs them. Just be sure to always buy the skill books in towns to get all of them opened up. Late game, more exclusive stuff for characters crops up too. You can get every single skill to max on everyone if you really want, so you can't screw up.
5. They're mostly just for extra character development, but a few will unlock stuff. Honestly, I would consult a guide there, your chance of randomly hitting a positive effect is very slim.
6. It is a bit. Late SNES game, trying to push 2D to the limit, doesn't always work.
Star Ocean isn't the amazing long-lost classic some people will hope for, I'm afraid, but it was the first in an excellent series. The later games really do get much better (and then worse again).