It’s been like this for a long time ~2014 if you try to live in Thailand on the wrong visa. I was once denied entry at the airport because obviously I wasn’t a tourist anymore, but I eventually got the proper visa and haven’t had an issue since.
I don't think so. Once you pass immigration, you have technically left the country. They couldn't even stamp you for overstaying unless they use a stamp in the future.
You need to register the house using the blue book, and since it's probably in her name then she has to do it. Once it's done, you can complete your TM-30 using her login.