[TillE]

> Would it be illegal to put up a website

> Is there some law stating that if you host a website

You're looking at this backwards.

The TOS is not a contract that automatically applies to everyone; I don't have to agree to it if I link to your site.

Generally, if you want to prevent people from using your website in a certain way (that's not blatant abuse/hacking/etc), you're going to have to resort to technical solutions, because your only legal recourse is copyright law, which may or may not apply.