he's getting married and getting a visa for that. Spending the money for a class and going through the trouble of getting an education visa makes zero sense.
Generally you'll need to use an agent to help you get the account open. Right now it's a little up in the air since that's mostly done in Pattaya but some of the agents there are no longer able to open accounts. It's possible by the time you're ready, it will be business as normal again.
Worst case scenario, you go to Laos or Cambodia and apply for the non-O visa there, then return and open your bank account for the extension.
She should apply for the 90 day non-O retirement visa before she goes to Thailand. This will make it easier for her to open the bank account she will require in order to apply for the 1-year extension.
If she tries to come as a tourist it will be impossible for her to open the bank account herself, and she'll need to find and pay an agent to do so.
1) That depends on the company that hires you. It requires hundreds of pages of documents to convert from a tourist to a non-B visa inside Thailand, and many companies either cannot or will not go through all that trouble. It takes very little paperwork comparatively to apply for a non-B visa at a Thai embassy outside of Thailand.
2) You can only work when you both a work permit, and a visa that is not work restricted. Many employers will say it's okay to work while everything is processing, but that's not true. They don't care though as they aren't the ones risking deportation.