Adsense are independent of IP. But, there are other risks involved, like getting the whole account banned if one of your sites break the TOS.
Course that will happen regardless of the IPs of the servers. I have multiple sites (not a lot) on the same IP, virtual hosts. Never has been a problem, and I've even linked from one to the other since they are somewhat related. Only 3 links among thousands of pages, though, so certainly not extensive. Again, never has been a problem, it all has to do with whether or not you follow TOS and Policies. As far as linking goes, Google is NOT stupid, they can easily tell if you're doing it for juice or if there is a valid reason for the link.
Not at all. As long as you play by the TOS rules you will be fine. Google wants to make money just like you.
You can host as many sites as you wish under the same IP. It will not give you any negative effects according to Google adsense TOS. If you meant for seo purpose and cross linking across themselves then I would recommend you to avoid doing it. Google can detect how gaming you are, even in different class C ip.
There is another concern regards hosting all of your sites on one host server account (which is implied by having just one IP address). What happens if that server gets a virus or your host has some other downtime problem? I have my websites spread over several different host accounts. And that saved me from some serious loss of revenue when one of the host accounts got a virus. Only a few of my sites were thus out of commission until the problem could be resolved. While dealing with this problem - my host told me that they are attacked all the time, most of attacks are rebuffed, but... While Google may not have a problem with hosting several sites through one IP address - as your revenue grows you still might want to diversify where you host your sites.
Some good and valid points. I prefer to mirror my content to a secondary machine such that if something happens to the first...well, switch and go. Where all on the same machine could be a problem is if the sites start competing against each other in terms of system resources.