Is it legal for the lender to keep adding fees after the account is charged off?

It depends on the contract between the credit grantor and consumer, type of account and applicable state and Federal Laws. Many federal and state regulations, as well as card holder agreements, allow interest penalties to accrue.

Yes.

A charge off does not mean the debt is not owed and subject to collection.

It indicates that the original creditor is closing the account for tax and accounting purposes and is referring the delinquent account to collections.