What is going to happen if I buy a domain name with page rank let's say PR3. And redirect it to another new domain name that has PR0, will the PR be transferred? And at the next PR update will it go up for the PR0 website?
301 (permanent) redirect does pass page rank (PR), however it will not happen instantaneously. It can take anywhere between 15 days to up to 3 months for it to happen.