Do I keep or discard extra successes? For instance, I'm fighting an enemy, and I roll several Crit die (lucky me!), ending up with 5 successes. However, I only need 2 successes to kill the enemy. Do I get to keep the 3 remaining successes (up to a max of 5) or do I discard them? Thanks!

I believe the extra success, in this case being damage is wasted.

The max 5 is for success tokens which you get from being aided by another hero or specific game instruction

Not sure I understand your question...but you dont get success tokens from hitting(rolling success's) the enemy do you(unless the card states 'gain success token)?

Played 1 full game and I took it you dont get success tokens for success rolls...they are just damage caused?