WordPress in Subdirectory of existing IIS Website

What is the process for having a wordpress blog as a virtual subdirectory of an existing site?

I currently have an ASP.NET website, mysite.com hosted on IIS, and I would like to display the wordpress blog under mysite.com/blog. Obviously the links and all should work also.

(I should note, right now, I have the wordpress site domain as blog.mysite.com (with no installation in my end).

First of all, is this possible, without installing wordpress and just by some settings in wordpress admin?

If I need to install it, does the wordpress installation need to be on the same server as my existing site?

Once installed, how do I get the wordpress site to display as a subdirectory of my existing site, as in mysite.com/blog.