Stablecoins like USDC are backed by FIAT at 1:1, so if you run into any issues like the ones you mentioned, Circle as the issuer of USDC has full responsibility to compensate you for your money, so there should be no worries.
This new Base L2 network by Coinbase, does it have its own native network token coin?
So far they have not issued their native token, and it is possible that they will never have one.