Yes with a Non O visa you’ll be able to open a bank account. You might have to visit a couple of branches as some also ask for a one year extension, but you’ll succeed as I did last month with a Non O in Bangkok Bank Jomtien.
If you apply for the initial 90 days Non O visa the funds has to be in your account at date when you apply. (Jomtien requires two months seasoning also for the initial visa).
For your one year extension of stay the funds needs to be seasoned for two months to apply.
I agree, the visa itself expires when it gives you a 90 days stamp or stay upon entry. And he’ll need to bank the required amount within the first month in order to get two months seasoning for apply.
The multiple entry option for Non O is removed in the e-visa system. You can apply for the one year extension of stay in Thailand and purchase multiple re-entry permits.
The page I posted still describes the formal requirements for applying for Non O e-visa through the Thai Embassy of London. For applying for the e-visa you use the site Brandon provided.