But I'll reconsider if I manage to get a proper barrier between the finances of the site and my own.
second, call them up and talk to someone. it's called 'business development'. you can negotiate anything. just say this part really scares you, and that you want to edit it, and that it may even be illegal in europe.
business protip: send them a european-legal version of their own contract that you feel comfortable signing. they might just say "sure, let's use this." -- it really can be that simple. you might find out they're planning an expansion into europe and you're their first partner.
and yes, form a limited liability company or a corporation, don't put your own money at risk. there's way, way scarier things in the world than newegg's marketing department, i assure you.
(Yes, it's great that you're reading the full terms of agreements. Too many people don't. But at the same time, you can't let ambiguous worst-case what-ifs paralyze you in business, or you'll never get anywhere. You can't steal second base while keeping your foot safely on first and all that.)