1) No. But once you have the domain and have vbulletin installed, you do need to enter the domain.
2) The license is for one site only. You cannot have two different installations at two different locations. If you have it up at yoursite.com and later move that same installation to yoursite2.com, then you need to change that location in your members area at vb.com and also remove the installation of vb at yoursite.com
3) You can host it wherever you want.
When you purchase an owned license, it allows you to run the software indefinitely. However, if you want to get updates after the first year, then you need to pay the renewal fee.
Here is the sales faq -
http://www.vbulletin.com/faqsales.php