Do sleep centers accept Medicare?

Yes, in fact many of them do accept medicare without exception. Medicare also helps pay for DME equipment like CPAP machines and mask with a small accompanying copay.

Yes, medicare covers sleep studies.

Yes. Most sleep centers accept Medicare. If you contact a center and find that it does not accept Medicare, you are quite likely to find another one in your region that will.

Most Sleep Centers and most sleep doctors accept Medicare. I am sure there are some exceptions but a phone call to them should give you the answer.