No it does not. The only time is lost is when the google PR updates come around. New owners and or transfers do not determine a PR at the time of said transfer and or ownership. Pfft even many domains that drop and expire retain PR.
PR isnt based on the owner lol, the domains, then if owners were based on PR then i'd have 15 domains with PR3 or more lol
PR do not always stay the same, it can go up or down and would be updated when Google updates their database.
Nope you're wrong. It's based on the incoming links. Often when a domain expires it loose some of the links this causes a little drop in the Pagerank.
No it doesn't. Even if the domain gets expired, the PR remains same for few months, but you need to make use of the backlinks or else they will be lost and your domain will come to PR0
If you buy an expired domains take a look into the wayback machine. Often you can find a "links page" ...copy the links there and upload them at your new website under the same filename.