Ok, so when you enter Thailand on the 3rd March 2020 you should be stamped in for a year. Before you leave the country again you should get a re-entry permit which will keep your permission to stay as it is then. Covering you till 2nd March 2021.
Your visa is multiple entry and is valid for a year. That means that during that year you can enter Thailand multiple times. You do not need a re-entry permit during the validity of the visa.
If you're not staying in a hotel, then you don't need to book a hotel to satisfy the immigration requirements on a visa exempt entry. Seeing as you're a visitor (not living here on back to back tourist visas or exempt entries) it's extremely unlikely you will be asked for anything and, on the TM6 form, you can just fill in the address of the house you will be staying at. I've been doing exactly that for over eight years.
Even before the E-visa system the London embassy have been pointing people to the O-A visa if they say they want to retire in Thailand. I know people who were flat out refused an application for a Non-O based on retirement years ago and were instead pointed towards the O-A. They converted in country instead and then obtained an extension of stay.