What are the visa rules for arriving in Thailand without a visa after March, and can I extend it or leave during the application process for a Non-O retirement visa?

at this time the 45 day visa exempt entry program is set to expire Mar 31, BUT the Tourism Authority of Thailand (TAT) has proposed it be continued until the end of the year. WATCH the news to see if they continue it or not.

If you show up here without having bought a visa from the thai consulate in your country before you come you will get stamped in on a visa exempt entry, you can get one 30 day extension on that for 1900baht at the immigration office where you stay.

You would get your funds and documents in order and apply for the 90 day Non-O visa when you have between 15 and 21 days left on your current stamp (it goes under review for that amount of time, you pay the 2000baht, wait the under review period then you go back and get the Non-O visa and a new 90 day stamp inked in.

NOTE: You CANNOT leave the country while this initial 90 day Non-O is under review (the 2 or 3 weeks)

AFTER you get the Non-O and new 90 day stamp inked in IF you need to leave the country during that 90 days you would buy a re-entry permit (that is ONLY good for those 90 days) and that will let you exit/re-enter and not lose that 90 day stamp. A single re-entry permit costs 1000baht

You apply for the year extension on that 90 day stamp when you have 30 days or less left on the stamp for 1900baht at the immigration office

March 31 is currently the cut-off, after that it is 30 days unless they extend the deadline.

Yes, you can extend it at Immigration.