Only in the sense that a higher page rank may lead to higher ranking in the SERPs, which may lead to higher traffic to your site, which could lead to more clicks on the ads. But there are sites with low PR and high traffic, and sites with high PR and low traffic. So the short answer is not really. The most important thing is lots of good quality traffic - from organic searches and from the US preferably.
no it doesn not change the click value. However as mentioned above you will get more traffic and clicks by having better PR and trafic.
You should worry about driving related traffic to your sites. This will give you more clicks and hence more revenue. Don't try to understand the great google, just try to get as many click through as possible.
I think the secret is the same with a broader range of ad display...not just google. Write good content, and/or have a site where the people who do visit...end up liking it. Adsense farms can make some money, but solid content is the not so shortcut way to earnings.