In my state we vote by mail and the outside envelope needs to be signed by the voter. The signature on the envelope is checked against the signature on file when registering and if they don't match the ballot is not accepted. I'm not sure how that requirement could/would be changed.
It depends what retirement system she was under. Employees under the CSRS did not pay into SS, but did pay into medicare. Employees under the FERS did pay into SS as well as medicare. It looks like she may have had some federal service under each of the retirement systems.
I believe the way it would work is you would suspend your FEHB and choose a commercially available advantage plan. You would then be paying for medicare Part B plus any charge for the advantage plan.