You can do your test and go in Chiang Mai if your international flight flies directly into Chiang Mai (not through Bangkok). As of today, the only international flight into Chiang Mai is through Singapore. Hoping more will be added over time.
Don't worry about your passport number not being on your certificate. That's actually quite common for the U.S. CDC certificates, or whatever you have from the clinic that gave you your vaccine. Our certificate doesn't have our passport number, and it's not a problem for the thailand pass.
Just one international flight in from Singapore. So if coming directly from Singapore, you can do your Day 1 here in CM. Lots of options in town. Several friends booked with Stay with Nimman.
Data point: ProLanguage charges 15K for the conversion fee in-country (TR->ED). They do all the paperwork associated with the conversion. Another language school I know charges close to that. Then add tuition, books, and costs for each subsequent 90-day renewal depending on how long you want to be on the ED visa.
I would agree. Many people have filters in their homes, and it can be pretty thick some mornings. I wear contact lenses and those sometimes get a bit irritated on the bad days. That season doesn't last too long though.