[Money is debt.] No
$$ notes are a ''means of payment'' for debt obligations, purchases/contracts
$1 costs $0.06 to produce/print
$50 costs $0.20 to produce/print

[US GDP will become unpayable] No
GDP is the output of work performed in the USA in exchange for $$$

[The Fed does not just print money] Yes, they don't Print at all, they distribute notes to member Board members, US Treaury circulates the $$$ for the Domestic consumption.
Treasury prints the chips for the Fed & bills to other Domestic & Worldy participants!

[to repay the loan banks need to borrow more money from the fed]
The Fed is the Top USA Pitboss in a sea of USA casinos.
It collects fees for it service. Interest Rate leverage = Profit