All of the previous comments presumed virtual private servers, as far as I could tell. I am basically wondering if arc (or another lisp) could be run on a host such as DreamHost via fastcgi, or a similar method. Since python and ruby are run on DreamHost this way, it seems feasible, and I was wondering if anyone else had done this with arc or another lisp.
Poking around the DreamHost support wiki and terms of service, I can't see anything stopping you. You can run an Arc interpreter in the background, so long as it doesn't eat too many resources, and I can't see anything stopping you from forwarding requests to it.
However, it will not be officially supported in the same way that Ruby and Python are, so you'll be on your own when it comes to fixing problems. It might be better to use their private hosting service so that they don't complain about your Arc process (which they may do if a bug causes it to behave badly). Although this means it runs on a private virtual server, you still get all the same support and software as with the shared service.
Another option is if your provider will forward web requests that come in on the standard HTTP port 80 for your domain to your Arc process listening on a port such as 8080.
I would assume so. I've used Apache's ProxyPass frequently and haven't had a problem. There's no technical reason that I know of that it would be either faster or slower than fastcgi. In both cases Apache is passing on the request to a persistent process. I haven't measured it though.
You'd need to find a provider who allowed you to install executables, so that you could install MzScheme. Then, I haven't heard that anyone has implemented the fastcgi protocol for Arc, so you'd need to implement that.
I haven't tried it, so I don't know, but in general I've found it easy to call MzScheme code from inside of Arc.
You can add xdef's to ac.scm; Anarki has a $ macro to call into MzScheme if you use Anarki; and I describe my favorite way to call into MzScheme here: http://arclanguage.org/item?id=8719