But when Carol redeems them, does the mint know now that Carol's IP has 10k sats?
Sure. Every denomination issued by the mint has its own signing key.
Also, when Carol decides to exchange these tokens for sats, can Micromanager Bob know through her IP that she is transacting with an outer LN?
Carol's tokens are simply claims on the sats in Bob's channel. If Carol wants to take Bob's sats out of his channel, of course Bob will know.