Yes they can, as long as you dont get too many of them, you will still gain benefit, but ideally relevant links are better.
yes, but take all factors into account -- a non related pr 5 link is better than a related pr0 link and 100 related links may be better than 1000 non related....its really a case by case thing and there are 100 variables at work
Most links act as a vote and have a certain amount of PR and link juice but obviously higher PR and relevant site links are king. Why not test? Set up two pages on two seperate websites using same titles and use the keywords in meta's and the page copy and then link back to one page using say 10 links using your anchor text from non relevant sites and then get say 2 links back to your other site using the same anchor text from relevant sites. Then see which page ranks higher for that term. This I would say will give you an indication of just how much more powerful relevant links are. Here's hoping anyway!
Going to have to change my way of thinking slightly, thought all one way backlinks were good no matter if relevant to the site in question or not.
Yes, they help. They also help in massive quantities. Today's algo's do not detect relevancy, but this may change down the road. For those that don't believe (or want to verify), look at the footer link on this page. Now see where that site ranks for "search engine optimization." Farming and SEO go hand in hand. Many of the sites in highly competitive niches employ the same tactics - purchasing one outbound footer link on the homepage of sites with PR. Today the practice is quite effective, but may result in tomorrow's ban.
I believe that is the linked text. So if you have a text link that says "SEO Optimization" then "SEO Optimization" is the anchor
Every links without nofollow are counted as back links for your website, the only thing is matter to get high pr is relevancy of links and quality of links.
Yes it helps. But it would be better if you can get links from related forums and blog. You'll get benefit in SERP and also can get targeted audience on forums and blogs.