1) The chain number you are seeing is just the number of the same type of enemy you have killed. The larger this number the better loot they drop as well as HP & MP restorations. As for the continuous attacks, they are mostly based on weapons. Katanas, Ninja Swords, and Pole arms have the highest multiple hit rates. Their may be other factors stat wise but I haven't delved into it too much so I'll leave that for someone else to explain. Note that Projectile based weapons don't multi hit, rather they have high critical hit rates.

2) Their is only a slight difference between character's and their weapon preferneces and I do mean slight, you won't really notice unless you experiment and have your characters use specific weapons for a while. Balthier seems to have a rather high critical hit rate with guns as Fran does with bows. As does Vaan has a high chance of doing multi hits with weapons.