NSF personnel funding If I request say 3 months summer salary at the rate I'm being paid by my academic institution, where would that money come from?

(a) Would I be paid directly from NSF?

(b) Would the NSF pay my institution, and then my institution funnels that money to me?

(c) Would my institution pay me directly from its budget?
The money will come as a grant to your institution, from which you can take summer salary.

Note that if you are in a position where “summer salary” is relevant, you are probably subject to the NSF limit that you can only have two months a year on your NSF budgets, and also that for many (most?) programs, you are unlikely to get more than one month a year on any single grant.