Could having my websites on the same server as someone who is violating the google TOS get my websites banned / penalized (assuming they aren't linking to the site violating google's TOS, just on the same IP)? A friend who I'm hosting is doing some stupid crap that would get him banned if caught, and I'm not sure if I should remove him from my server in-case it might effect my websites on that server if his sites get banned.
No you will be fine, Google understands the large majority of websites are hosted in a shared environment and people have no control over who's sharing the server. So long as there's no connection such as Interlinking, Adsense PUB ID, Analytics Account, Whois Details etc. The only problem it may cause is if he's sending large volumes of spam, your server can get flagged as a bad egg and your legit mail goes to peoples junk folder.