Of course there can be liquidity crisis in fiat system. We just witnessed one in 2008.
No the Fed does not print money to "buy debt". If you are talking about QE that was to inject liquidity into the system by swapping asset for reserves.
Bitcoin can't avoid liquidity crisis. As a matter of fact it would be more prone to liquidity crisis because of its inelasticity
Low liquidity would result in bitcoin's price increasing. Wouldn't this automatically solve the liquidity issue?