These are domains as usual and MyDomain.com is a normal domain registrar so dont worry about any of that. The only thing is that you cannot move it before 2005, but naturally you can host the site(s) anywhere you like. Just set the nameservers accordingly.
About those cookies.. well that ain’t my speciality so I cant begin to guess whats up with that, but the site works fine for me.. allthough a bit busy right now.. wonder why 