You must be legally married before applying for a marriage visa from outside of Thailand or for an extension of stay based on marriage from inside Thailand.
You should be able to open a bank account yourself, even if you are on a tourist visa or visa exempt stamp. All banks have different requirements. All branches have different requirements. Even within a branch two staff members may give very different answers. Find a branch of the bank you want (I use Bangkok Bank in Doi Saket), in an area with lots of foreigners. Go to the bank with your passport and a friend who holds an account at that branch. Have 100,000 thb to deposit. Should work but many banks/branches will also require a certificate of residence from Immigration. But instead, you could offer a letter from your hotel/ hostel/ Airbnb/ friends house stating that you stay there.
You could apply for an extension of stay based on being married to a Thai citizen. Extension of stay based on being over 50 years requires 800,000 thb in the bank but needs jumping through ,uch less hoops so in my opinion is the better option.
My Australian friend died in Chiang Mai without having a valid will for Thailand. His Thai widow had to employ a lawyer to go to the Thai courts for release of his banked money (mainly his 800.000 thb for his retirement visa. It took a full 12 months to get access to his funds,