1. Yeh, all the ultimate weapons have something that powers them up.

Cloud's Ultima Weapon: The more HP Cloud has, the more damage it does.

Barret's Missing Score: The more materia equipped on the weapon, the more damage it does.

Tifa's Premium Heart: The more Misses you get while using her limit break, the more powerful it gets.

Red XIII's Limited Moon: The more MP he has, the more damage it does.

Cid's Venus Gospel: Same as Red XIII.

Cait Sith's HP Shout: Same as the above two strangely.

Yuffie's Conformer: Does more damage if the enemy she's attacking has more experience than her.

2. I'm pretty sure this isn't true as aren't all attacks done by the party capped at 9,999 damage?

3. If I'm not mistaken, this only works with Independant materia like HP PLUS, MP PLUS, etc.