You can host on your own, or you can use Sawtooth Software hosting. If you have an annual subscription for your Sawtooth Software products, then you can host for free.
Yes, you can host your survey at multiple different web domains.
If you use Sawtooth Software hosting, the survey will be hosted on a system of multiple servers. You may also set up your survey on a similar system, but it is very complex and may not be worth the effort.