A. No, you can no longer contribute to your HSA because you can only contribute tax-free dollars to an HSA if you have a high-deductible plan and no other health coverage.
If you enroll in Medicare, you can still use HSA money to pay for out of pocket costs, but you cannot continue to make contributions to it.
Note, you can still contribute to FSA, but you do have to use the FSA dollars in the same or following year.