What increase will I expect if I have a PR0 site that has a backlink from one PR7? The PR7 site has no relevence to the PR0 site. Will I see a large jump to 5 ish or only about 2-3? I am talking about only the 1 link,there are other links but they are from PR0 sites (about 10 ish) and are also irelevent. The PR7 site is a very very strong PR7 site with backlinks from many PR 8 + 9 sites.
It depends on how strong that pr 7 page is and how many outbound links are on the same page as the pr7. Ex. If your is the only site that page is linking to, your site will most likely gain a pr 6. So the more sites that page links to, the less pr your site will receive.
Yes, your PR will go up with that link. Since it's not a relevant link for your site, it will likely not get you much higher in the serps though. Don't buy this link if the other sites being linked to are garbage. You want your link in 'a good neighbourhoud'.
Load up your site (and your potential incoming link) in URLtrends.com to get an idea of the estimated idea of how much PR each outgoing link passes along.
I disagree with this, I havent seen much evidence that relevency makes a difference yet for backlinks.