IIS subsite is the way to go, its easier to install and you won't have to code anything.
My answers below:
-Sharing templates/partials in main site and forums subsite
create a template "mocking" your main site layout.
-Sharing css/images/downloads, basically any links/assets/resources across main site and forum subsite
No problem, if you are in a subsite inside iis, you can use a path related to the domain like /styles/main-site.css
-Adapting Nearforums into the Responsive Design of the current site - maintaining consistent look and feel
-Cross site authorization
Check out this tutorial: How to authenticate users from an existing db into Nearforums site
-Routing across main site and forum subsite
Main site and forum sub application would be 2 different applications in the same IIS website. It won't affect each other. You should create your main site without taking care of the subsite.
-Using MvcSiteMapProvider to build dynamic navigation and menus
I'm not really aware about how it works...