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.
If you are on a Windows host yes they will need have it installed for it to work. I'm fairly certain that the shared Windows hosts would have this installed anyway - it's an essential part of IIS!