here's a good recap of whether or not those links will hurt you: http://www.seroundtable.com/archives/014953.html
free sites can't, spammy sites might, be it free or otherwise and its not the link count, your links are counted either ways your site on the other hands might not get the expected PR
Backlinks from quality sites always improves your pagerank. It doesn't matter if it is free site or not.
It definitely won't. What give you the idea that it will. In fact some high PR site located on free host could even benefit you and passing link juice especially if it is related to your niche.
Internal links...You can't control them. And if they are located on loe reputable sites Google won't decrease your PR!
there are plenty of good quality high PR sites running on free hosts. any backlink is helpfull as long as its not from bad neighbourhood