I think the answer here is:
AMEND
First riddle:
My prefix comes at my suffix
Your prefix is AMEN which is the closing word that usually comes at (your suffix) the END of a prayer.
But the guys that are my infix
Demand that we add some fixes!
Your infix is MEN ('guys').
Second riddle:
My suffix fixes what was broken
To MEND means 'to fix'.
My prefix and infix badly answer
The question we are trying to improve: What am I?
If your prefix is AM and your infix is ME then '(I) AM ME' is certainly a bad answer to the question 'What am I?' as it gives us no clarity or new information at all!