The coop is not a seo tool, it is used to advertise your site, so you should not try to gain PR with it.
I suppose in theory it is possible but as fryman said it is by no means the purpose of it so don't use it expecting a PR increase
Since the ads rotate it would be very difficult to gain PR with it, at least until most of the users change to static links, which doesn't seem to be happening.
Purpose of coop is not to gain PR, but pages do gain in PR because of the links. I had 25K weight pointed at 1 page with several anchors during June/July and in the PR update of July the PR went from 2 to 6.
I've had PR increases solely from the coop as well. mightyb: that depends more on google than the coop as long as you've been running the ads on the coop for a while before an update, you'll most likely gain PR (assuming of course you have a decent amount of weight)
And it'll be worth just as much. Value of site whose pr is based soley on coop weight I'd say is worth no more than the website if it were pr0 (just on a pr basis, not dealing with serp benefits )
With the right amount of weight, you can easily increase PR. I have three PR6 sites. Two I started in January and the first PR update after the February 2005 time frame, one went to PR6, the other to PR5. The third site was already a PR3 and moved to a PR6. On the other side of that though, the PR didn't mean a thing. Two sites with PR6 and barely 30 uniques per day. They all now get 300-500 uniques per day (still not enough, for me). I'd rather have more traffic. PR does not necessarily mean more traffic.
I have no idea. These were three links of 30-40, but I had most of the weight on these three sites. Total weight around that time was 120k (weight was different back then, that's probably 30k by today's weight standards).