Verified answer

"If I were to not get the full blown NROTC Scholarship would I need to apply separately to the university's NROTC program? "

Not for the NROTC program, but for the university itself...yes.

"What if I were to choose to go non-scholarship right off the bat? Would I still apply for the scholar ship or do I apply to the university's NROTC program?"

Both, actually, thanks to a recent change in policy. You would apply to join for the unit (which isn't that hard), and once there, apply for the scholarship separately.