You don't need any kind of visa to take classes in Thailand. You can take Thai language courses if you want.
A bank account will be dependent upon your visa. But you already have a 5 year visa. You would have to find a way to get your existing visa cancelled which can prove challenging. But that's not guaranteed to make any difference anyways. A Thai language visa will only ever give you 90 days at a time to stay in Thailand and many reports that banks are not willing to open accounts for people on Thai language visas. Those reports started long before the current situation with bank accounts.
You're using the wrong terminology, and that's why you're not finding the correct information. You already have the retirement visa. That's what the non-O visa is. There is no more visa. You won't have a visa again after this. That visa was used when you entered Thailand. From now on you will be applying for extensions. An extension does not require 15 days or any amount of days to apply. You can apply on the last day of your permission stamp in your passport (not advised to do so). Retirement extensions are usually given the same day you apply, no need for the 15 days because there is no "under consideration" period.
The 15 days is only needed when you are converting from tourist to a non-O retirement visa (which you already have).
Any day is fine, as long as it shows as received within that month. Earlier is better though in case you experience some type of delay with your transfer, so it doesn't slip into the following month and ruin all your progress.
Only if you're trying to use proof of monthly transfers for your 2nd year retirement extension. Otherwise you can use embassy verified income (if your embassy provides this service) or proof of 800,000 baht in your Thank bank account for the required amount of time.
Embassies don't really have a mechanism to issue a visa for less than the legally mandated duration. The DTV law states that a DTV is valid for 5 years. So it should be issued for 5 years.