Yes, it restarts for each newly targeted enemy.
Initially, I suppose, this was used to keep bosses from throwing their best skills at you the moment they see you.
I doubt that it overrides the delay, though. Interesing thought, but from what I've seen that does work just like a cooldown. So I guess if you have both, it just checks the conditions separately.
Yes bumbleguppy, all you need to upload are the arcs and arz files. I wish I knew why the DBRs are built into your build directory, mine does it too