wiki web access

Be careful what you ask - or at least how you ask it.

Could I use out host-monster hosting to point a domain such as our domain.com/wiki to our osx wiki?

yes, but it's complex and probably not what you need.

Since all traffic for 'domain.com' will go to the hosted server, the hosted server would have to look at the request, determine that it's a request for a /wiki page, and then probably proxy the connection to retrieve the page from you and return it to the user.

So yes, it can be done, but it would be far, far easier to just setup a new hostname in your domain, e.g. 'wiki.domain.com' and have that point to your server (potentially through port forwarding in your router.

Then users only have to hit http://wiki.domain.com/ to get to your wiki server, or use http://domain.com/ to get to your regular web site.

So you don't need another domain, you just need a new hostname in your existing domain that points to your server. Whoever manages your DNS should be able to do this for you in minutes.

Yes - you'll need to tell your router to accept connections on the public port 80 and forward them to your server. The specifics/mechanics of this will be buried in the admin interface of the router, each make/model of which works slightly differently.

You may also find that your router is incapable of forwarding requests from clients on the internal network back to the internal server so make sure you test this from outside your network first, then you can resolve the internal clients issue.