Already partnered - that the "Internet-Explorer" tag already has an image indicates an existing partnership [1]. This may be a deeper partnership though.
Wouldn't have to be. You don't have to partner with SO to allow folks to ask questions about your product; they just have to be programming questions. Ideally good ones. Also helps a lot if you answer them.
If you want to go further than that, there are various levels of sponsorship possible for a tag, and [internet-explorer] has been sponsored at some level for at least a year. These grant you various advertising and branding privileges, but do not otherwise affect how questions are asked/answered within that tag.
Disclaimer: I work for Stack Exchange but am not involved in the sales or marketing side of things.
Definitely. It was created by Jeff Atwood who is a very "pro-Microsoft" figurehead in the .NET community so there was probably a lot of collaboration in this move.
As catkin has pointed out, Jeff left SE a good while ago. Also his current baby, Discourse [0], is built on Ruby on Rails, Postgres, Redis at the back end and ember.js on the front [1].
1: http://meta.stackexchange.com/questions/30187/what-do-icons-...