Retiring in 2023, have a couple of HSA questions

I'm retiring at age 65 in June. My wife and I are both covered by a family HDHP. I am the one with the HSA, she is already retired. I have been funding my HSA to the maximum allowed via payroll deduction. I want to put the maximum I can into my HSA for 2023, but I need clarity;

 

- Is it correct that I can only put 5/12's of the maximum in my HSA since I'm retiring June 6th? 

- I plan to file for my Medicare when the window opens for me in March. Will the date of my application affect how much I can fund my HSA in 2023? In other words, should I delay making application for Medicare on March 6th and wait until I'm actually 65, three months later?

- Can I just do an IRA rollover now and fund my HSA to the yearly max?

- Is there any way to get around the 6 month lookback period for an IRA to HSA rollover?

 

TIA for the considered reply or any strategy suggestions as I wrap up my working life and head to Medicare.

Tim