Chrono Cross Battle Mechanics Q

I understand all the basics but I don't get some things. Anyone who has stamina can go, but what determines when the enemies go? Is it just random? Do they have their own stamina bars that fill up as you attack them?

And how come sometimes when I run up and attack people and the monsters interupt my attack to do their own, my character will run back up to where he was and continue from his latest gained hit % but sometimes they will go back to standing in the line and all my hit % will have reset. I'm highly confused :p

And what is agility for? Not for evasion, since evasion% is for that... Hmm.

Each enemy has its own stamina bar. When its bar is full, they act immediately. This may interrupt your character's attack. If the enemy's attack hits your character, your % will reset, otherwise, it will stay as it is.

Who-ho...I gotcha. Thanks :D