1) No, I think that you're wrong about the first one. Monsters give out a set amount of exp to people that participate, and however many take a turn during a battle get that much. If a monster gives 5 exp, and three members take turns, they'll each get five. if all seven take a turn, they'll still get 5 a piece. Use everyone in each battle if you can.

2) You can get some rare items through blitzball, Wakka's other three over drives, his celestial weapon, and the sigil to finish powering it up. The jupiter sigil shows up after you have all his overdrives, and you play tournaments to get those. If you reset after each match, eventually it'd show up without you having to play many games. (I think the lowest possible is 26?)

3) Weapons are more or less alike. Whatever listed abilities it has it has. They don't have inherent stats, just what they come with (which is always listed) or what you customize them with. You'll get to customization a bit later.

4) You have quite a bit of game left if you're just now fighting Sin at Operation Mi'ihen. You should ideally wait until you get to use the Airship permanently, since it'll be easier to capture monsters, but you could feasibly start after you capture the initial ten monsters at the Calm Lands. (Don Tonberry is one of each of the Sunked Cave monsters, iirc. You'd also want a overdrive->AP weapon for this.) You can do it as much as you like, really. Until you have 99 SP and nothing to do on the sphere grid