Upon using the /unrent command, or when the rent expires it should run a command setting all doors to true. If there is no easily accessible way to set all doors to true you could have a world edit command run. This command taking a top corner block and its opposing bottom corner block and running /replace door air for all door ids. if that is also not easily accessible (because I couldn't find the variables for it on areashop) then perhaps on unrent it would set flags to allow everyone access to doors in the region.
I like this. Helps to see if there's an empty room that's all by its lonesome unable to be rented due to a closed door.
Not only that. You have to know the region name or actually be in the region to rent it. Making many regions inaccessible
It's true, sometimes I had to make a ticket to know the name. (And one time it was owned by the staff who came lol @Omnomivore)
Remember that AreaShop is NOT a Massivecraft plugin so the staff only have so much they can do to customize the features
That is not a possibility unfortunatley, to unlock MassiveLocks with Areashop extensive work would be required. For now I can just suggest you use the area Shop list for rentable properties