if you purchase PPC ads, say on Facebook - can that help your page rank? or is Google able to see when a link is a PPC ad vs when a link is a free one...
No. Probably not. Here is why: When determining whether your site will get pagerank for a link to it, Google waits to be sure the link exists for awhile (weeks or months). That is, the Google spider checks each time it visits a page to see what links are on it. With PPC, your ad (link) may not be on the page the next few times the Google spider comes by, so you wouldn't get credit for it (it won't help your pagerank).
I'm sure google knows if a link was given through ads, link exchange, 3-way or anything. Better get PPC ads on site highly related to your site so you can also get higher quality of visitors.
Adsense ads are links, but those aren`t hard links. (they aren`t static) I can be sure google doesn`t consider them at all. I think that the google spiders don`t even take those links into consideration, they are paid links and not staying there for months nor years.
NO it will not help! PPC links are not links to your site. They are links to the PPC programs server that then redirects to your site. If you look at PPC ads the links is never a direct link, so there is no help for PR or SERPS. But why worry about PR? It really doesn’t mean anything anymore! I would worry much more about SERPS. And PPC, in the LONG run can help SERPS. HOW? If you run a highly targeted PPC campaign that leads to a high quality site you will have visitors that are happy with you site and some of them will link back to you! Not to mention they will buy what you are selling!
No it doesn't count as a vote coming from the site and it's just an advertisement placed over there. Definitely that won't affect page rank at all.