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.
Oh sorry see it's one booking but different airlines but still think that domestic flight will change things as far as Covid tests/entry to Thailand. Don't know if your bags would even be tagged all the way through. I'm not an expert though but just pointing out some things I think you need to look into...also if any of these flights get cancelled or delayed along the way what happens?
You also have flights within Malaysia so not sure how that works as you are not just landing at one and transiting out of county but rather flying domestically. It would change things I think if you have to clear immigration. Not sure if that's allowed or not. Probably have to do a little digging to find out.