If I have to install "IIS Rewrite Module 2.0" on my machine for it to work, since my web site runs on a shared web server, does that mean that my host has to have this installed in order for it to work on-line?
If you have a shared hosting package, you will not be able to install the Rewrite module yourself(if it is not pre-installed by your hosting provider).
Shared hosting packages have certain limitations and installing softwares or updates by the client is once of them.
Usually, IIS RW Module will be installed by your host.
Please check with them once. In case, it is not, you can request them to get it installed.