Non-Immigrant O visa stands for Non-Immigrant Other, but that Other must be specified, e.g. based on marriage with Thai national or based on retirement.
Of course, most Thai banks offer online banking. But in order to open the bank account, you have to apply in person, best advice to take your wife/girlfriend with you. Bangkok Bank for example requires a Thai SIM in order to receive the OTP, don't forget to open International Roaming for this Thai SIM, so you can do online banking from outside Thailand.
The Schengen-Visum of course still exists and is unaffected by Brexit. Also before the Brexit, the Schengen-Visum was not valid for entering the United Kingdom.
For receiving text messages, international roaming is of course required, too. How should the mobile connect to the network abroad if there is no roaming activated?
While it is true that everybody entering Thailand should have health insurance, buying a Non-O visa in the home country does NOT require health insurance -- in normal times of course.