The 2 month seasoning only applies to the extension in Chiang Mai. The op's problem is that Jomtien applies the 2 month seasoning to the initial Non-O application.
The 800k has nothing to do with the 90 day report. Either you've misunderstood - maybe the official means when you renew your visa you need 800k - or you're being scammed.
"Are there any other documents I’ll need to open a bank account? "
No. In fact, I doubt if they ask for all these documents. With Bangkok Bank, I think all they need is your passport, TM30 and rental contract.
"Do I immediately apply for a Non-O?"
If you've just extended your tourist visa, then yes. Immigration offices (Chiang Mai anyway) need, I think, 15 WORKING days to process your non-o, so that's 21 actual days. Your extension is for 30 days, so you need to go to immigration within 9 days of getting your extension.
"After I get the Non-O, do I wait 45 days to apply for the retirement visa? Or, am I waiting until I only have 45 days on my visa to apply for thr retirement visa? "
(You mean "to apply for the one year extension".)
You need to wait until you have less than 45 days left on your stay permit before applying for your one year extension.
"Is #2 in that photo asking for the residency certificate?"
No.
"Is #3 asking for my TM30?"
No, it's asking for your rental contract. But take your TM30 to the bank anyway.
You don't need to apply for a new non-O, you need to apply for a one year extension of stay. At the moment your stay permit expires on 18th July. You need to go to immigration and apply for the one year extension when you have no more than 30 days left on the stay permit (so after 18th June). Some immigration offices let you apply earlier, when you have no more than 45 days left.
On May 11th you just need to go with your passport and get your Non-O stamped in. No other documents. You'll get the Non-O visa stamp + 90 day stay permit.
When there are fewer than 45 days left on your stay permit, you can apply for the one year extension. THAT'S when you need all the same documents as before, plus a TM7 extension application form, plus 1900 baht. From your posted printout, that means any time after 8th June. You get the one year extension on the same day you apply.
This is normal. You may have "big trouble" next time, or you may not. Depends on the official. Also depends on the port of entry: Suvarnabhumi is notorious for having strict immigration officials. Don Muang MIGHT be better (not sure), provincial airports like Chiang Mai less strict, land entries even less strict.
By the way, getting a tourist visa is no guarantee of entry. If you want to stay in Thailand long term, you'll be best getting a long term visa.