We're told (in Buffy: Real Me) that a vampire can only enter a property when it's invited in by someone that lives there.
XANDER: Uh, yeah, actually, she -- Harmony -- kind of happened to sort of get an invite.
BUFFY: You guys can't invite her in. I mean, only someone who lives here can-
Buffy: Real Me
The barrier on the property ceases to function if and when the human residents die and, critically to your question, a new barrier is erected if a new set of human occupants takes up residence in a property that was previously accessible to the vampire, as seen in Angel: Heartthrob, where Angel, who was previously able to do a room-by-room check of the Hyperion, is now suddenly barred from entering Fred's room.
Angel: I can't come in.
Fred: Of course not. You're worn from your trip. You go rest. We'll catch up later.
Angel: Fred, I want to talk to you, I just can't come in unless you...
Fred: I invite you. Instead of being rude! Oh, come in. Come in.
Note also that mere ownership or technical residence of the property isn't sufficient to bar a vampire from entry, as seen in Buffy: The Freshman where vamps enter Buffy's dorm room freely, as contrasted with Buffy: The Yoko Factor where, a few months later, Angel needs an explicit invitation to enter the same room now that she's accepted it as where she lives (which also addresses your point #1, since he had entry rights to her house in Sunnydale, but not to her dorm room)