Each time you change address you have to do a new TM30 and you will have to do your 90 days report in person. You only get to do a 90 days report online if you didn’t change address since the last time.
Happened to me, I didn’t cancel my non-B extension and then came back for a non-O extension, they complained and cursed me because they had to do more paperwork but they did everything and I got my extension ¯\_(ツ)_/¯
The 90 days report has to be filled 90 days after you last entered the country or 90 after the last report you did. It’s not related to when you got your visa or extension but to the date on your entry stamp.
in theory your landlord is supposed to do a TM30 for any foreign staying one night or more, in practice if they stay only a short time and don’t have any business with immigration or the police they should be fine
you need to show proof you’ve been registered, they could look into their system but they won’t bother, the problem is that with the new system the landlord (or hotel) cannot look back more than a week to get your proof so they would have to register you again to be able to print out the proof if it’s been more than a week.