Possibly grip strength. Does it feel like they're getting pulled open? That would suggest grip strength. Heavy dumbbell rows for high reps tend to fix that. Using Fat Gripz on stuff like lat pull-downs has helped me recently as well.
You mean FSL set or plus sets? Plus sets aren't AMRAP sets, you should leave one or two reps in the tank.
Sufiandy is right in that if you reset quickly between reps (say maybe 5-7 seconds) and that's consistently how you pull for reps, it's fine. Any longer rests and you're basically doing cluster sets which is different.
I would recommend trying to learn how to pull without resets though, although it isn't essential.
Correct again. If you can't hit more than the minimum prescribed reps on your plus set without those resets, you've stalled and it's time to move your TM back about three cycles.