Yes, they are unique attacks with their own animation. They do not give a stat boost, although you do get a stat boost from party variety: each class has a stat they give +10 to which matches their main stat (minus Arcanist, which gives PIE.) You can only get each bonus once though, so the best way to go is to have a varied party so you get +10 to all stats.

As for chain bonuses, it's a bonus to xp for killing enemies in close succession.

Finally, one last note on limit break: the less duplicated classes you have, the faster it build. So, a paladin, warrior, white mage, scholar, and 4 different DPS fill it the fastest.