PD 365 uses the Cyberlink Application Manager and will initially install the latest version. It will notify you when there are updates and new media packs are available. You can refuse to upgrade but I am not sure for how long.
I would think you would be able to open your old files just fine. I think this because the templates off director zone say they will work with versions dating far back.
I am not too sure if you can use it offline, you probably need to connect every x days. I tried to lauch it once and it said I needed to connect to the internet to ensure my license was still valid. I am connected most of the time but I guess I was not at that time.