You cannot extend a non-O visa for 1 month. You can only apply for the 1-year extension, unless you're married to a Thai (then you can do the 60 day "visiting Thai family" extension).
There's no simply way to get 4 months in Thailand without doing a border bounce. For the least amount of hassle, suggest getting the non-O visa from the embassy, and just doing a border bounce and returning visa exempt after that.
You're correct. No need to do anything except exit Thailand. It's only long-term extensions where an upcoming extension is planned that really need to be transferred.
Then you'll receive 60 days at the airport. Do not go to "visa on arrival" window. Just go directly to passport control. Make sure you fill out a TDAC online within 3 days of your trip.
If you need the additional 30 days, you'll need to apply for the 30-day extension from immigration. In Bangkok that will be at the IT Square Laksi office if you arrive without a visa.
You can apply for a 90-day non-O visa if you qualify.
If you are from a visa exempt country, you can qualify for visa exempt entry which is a 60 day permission to stay stamp, and not a visa. This is meant as a short-term tourist entry. You can apply one time for a 30-day extension. If that meets your needs then you should be fine. If you need more time then you might need to look into other options.
Most foreigner accounts are not being frozen due to suspicious of scam though. All of this information is about accounts closed for that.
Most foreigner accounts have been frozen due to KYC, which was specifically called out as being separate from all these hotlines and phone numbers and people to contact for help.
The requirements for a CoR vary by immigration office. I don't know specifically what Jomtien asks for, but normally it's as you listed. TM30, passport, possibly rental agreement though I don't think that's normally required at most offices.
The price depends on the office and the time. For example some offices are free or very minimal charge if you wait for 1-2 weeks. But you can try asking if they can do it faster if you need it and they might offer an "express" service for 300-1000 baht.
Many DLT offices no longer accept yellow book for drivers license. That means you'll need to get a Certificate of Residence from immigration if your DLT has this policy. It will probably match the address of your TM30, which should be where your lease is.