Should be no problem. You will need a residency certificate from immigration specifically for opening a bank account. Bring copies of your passport pages, dress like you6r on business and your won't have any problem.
it takes one day! Go to immigration in the morning for a residence certificate, have copies of your passport info and you're in and out of the bank within the hour.
Just apply for evisa abroad for non-o. Then arrive on the non-o and you shouldn't have any difficulty opening a bank account to get your 12 month extension at the end of your initial 90 days.
much easier to apply for non-o in your home country. There are some catch 22's doing it I in country forcing you to use an agent and then being at their mercy for future extensions....
Most likely will not be able to get insurance in Thailand for a 79yr old. If you can find it, it will be exhorbently expensive.
If your intention is NOT for her to stay long term then best to get travel insurance from your home country and then arrive for 60 day visa exempt. You can extend it another 30 days when you're heading the end of your 60.