It is the property owners responsibility to file a TM30 within 24 hours of you arriving. They need the blue house registration book, ID card and your passport. The location of the property will not interest the Immigration officer. As has already been suggested it would be easier to check into a cheap hotel for a couple of nights.
The owner of the building is responsible for reporting a foreigner staying at his property within 24 hours of arrival. He/she will need the blue book house registration, ID card and your passport. If this has not been done I suggest you check into a cheap hotel for a couple of nights before you apply for the extension. Even though it is the building owners responsibility they will fine you so cheaper to stay in a hotel.
That's is not true. Hotels register you online. That is why they photo copy your passport when you check in. Immigration may want to see your proof of booking.
Unless she has a history of using a lot of visa-exempt entries she should be fine doing a border bounce. Rather than flying she could use an agency to take her to a land border. The agencies guarantee re-entry without problems.