Did fractional reserve banking occur during Linclon’s Greenback money era?
Yes, FRB was widely spread even before the greenbacks. The novelty of that era were the national banks, that could back their banknotes by federal debt; while all other banks were pushed out from issuing banknotes by a prohibitory tax. This to a degree centralized the banking industry. The suspension of payments in specie did not help either, and a large inflation followed - thanks to both the greenback and FRB.
See e.g. Rothbard’s History of Money and Banking in the united States.
It definitely did. If fractional reserve banking had been prohibited during that time, there would’ve been no need for green backs, and there also wouldn’t have been all of those Panics in the late 19th century/early 20th.