Whatever your reason is related to Covid. They may be able to help you at immigration.

And yes Covid extension first time from date applied

#2 not how it works Covid extensions are 60 days I think you are meaning the "under review time" but this isn't something you add up and can get at multiple immigration offices. I believe in Phuket you get your stamps same day (have also heard pick up passports next day) so just find out the process in Chiang Mai and decide from there. May be ideal go in Chiang Mai around 60 days before your fly out date and have stamps before heading to Phuket if transportation in Phuket is an issue for you. Do you have the list of everything you need?

I think a few weeks is best

Do you need to be on a visa in Thailand to get the police check? If you are here as visa exempt with extensions can you get one?

Philippines is allowing certain countries visa exempt for 30 days and must show proof of return or onward travel. You can apply for retirement visa if meet the requirements has to be done in advance then meeting booked once you enter country

Yes you need the main page and stamp page. Guess you could have left and found a low cost place to copy but for the convenience 100 baht isn't a lot of money.

You might get some good suggestions on here too for E language school based on your desired location.

If you come in 30 day exempt you can extend 30 days for 1900 baht but believe the 60 day or STV has to be done in advance. 60 day you can extend I believe 30 as well. There are many language schools just do a search by area you are staying and perhaps contact a few for ED Visa details. I believe many offer 3,6,12 month programs.