Alternator issues
#2
You're under spinning the alternator. An Underdrive pulley spins the alternator slower so it produces fewer amps. People fix this by replacing the pulley with a larger one or change the alternator to a more powerful unit such as a 200+amp. Another option you can plug it into a battery tender after each use to keep the battery topped off so you don't over drain it.
#3
As for the OP, I think he put an under drive pulley on because he’s revving to 7k rpm and it’s possible that the alternator he is using wasn’t designed to spin that fast, so he wanted to slow it down. That being said I have no clue how fast his can spin. However, I’d let it ride unless I was having charging issues.