My parents own a condo in Florida.  They filed a quit claim deed giving
me the property after they are deceased.  My question: Can they still
use the property as a means to obtain a loan?  (The condo is paid
for.)  And can they sign up for one of those reverse mortgages that
pays them to live there?

Technically they still own the property and may do with it what they
like, including a reverse mortgage. Upon their death however, the
title will not be clear until your parents' estate (or you) pay off
any loan against the property.