If I have a backlink on another site, does it only count if it is on their homepage? And how do I get a specific page to be crawled and indexed by google?
Yes use backlinkwatch this site will show you all the links which are posted by you. If your links are not shown then wait for some days because it takes time to index page on which you commented.
It doesn't matter as many backlinks you have. It matters where the backlinks come from. Check out the basic illustration of the PageRank algorithm: http://www.prlog.org/10235329-google-pagerank.png
That will still count as backlink. And ping your site so that it will help to indexed your page faster.
It counts if the link is on any of their pages and to get a page crawled you need to ping it with a program.
It will count on any of their pages inside, but for page rank, the page will consider and not the home page.
I think backlink-pagerank relationship is just based on the pages Google's bots frequently visit. I mean if these bots are suddenly focused on a page for a moment, the PR of that page booms. So I think what we should do is having backlinks that has Google bots much as guests : )