Medical Insurance

I had a HDHP plan with an HSA thru the marketplace thru May 2023.  As of June 1 I was enrolled in an health plan thru my employer.  Although I did not contribute to the HSA after May 31 I had distributions after that for bills incurred when I did.  About the same time, May 1st,  I became eligible for Medicare although I only opted for Part A.

My questions are: (A) Should I chose "yes" when asked If I had Medicare for any part of 2023? and (B) Should  I chose "Yes" when asked if I was over 65 when distribution was received? and lastly (C) which boxes do I check for each month after May?

Thanks!