As mentioned, it's up to the IO at the airport but as you have been away for 5 months, it's fairly clear that you are not trying to live here on visa exempt and extension stamps so you should be ok provided you have the 3 requirements when you arrive, if asked for them.
... you cannot get a re-entry permit on a visa exempt stamp. Once you stamp out that exempt stamp is void regardless of the days remaining on the stamp.
Yes almost certainly because your hotel TM30 will be logged with immigration and won't match your rental place when you go to do an extension or even a 90 day report.
You can only apply in another provence if you first get a new TM30 from the owner of the accommodation you are staying at, in that provence. You cannot apply with a TM30 issued in CM.