For some things, yes.
While most of their back-end servers are running Windows, NetCraft shows some servers (such as download.microsoft.com) as running Linux. This is most likely due to their use of Akamai for content delivery, which has caching Linux servers in front of all sites.
Microsoft also has a farm of 10,000+ Linux servers that host the Skype infrastructure.
Linux hosting involves hosting your website on a Linux based server in order to make use of additional coding and programing not available to other operating systems. You can find more information about Linux hosting at the Webhosting Top website.
In order for you to use Microsoft exchange hosting you have to have Microsoft windows server. As long as you have a windows on your computer you should be able to use Microsoft exchange hosting.
There is nothing that stops one from configuring Arch Linux to function as a server. It is not equipped to function as one in a default installation
Use Linux or Macs.
The Microsoft Exchange Server is an e-mail server used primarily for businesses. You can purchase it through Microsoft or a retailer that sells Microsoft. It is similar to your everyday e-mail, but it is not for personal use.
Yes. HTML, PHP, CSS, Javascript, etc... are all platform-agnostic. You could even host the website on a Linux server, and you would still be able to use it in Windows. Many sites do just that.
No. Universities use Microsoft Windows.
The Apache Foundation is most widely known for their Hypertext Transfer Protocol server.
Linux.
You don't, it's a Microsoft product that runs on the Windows family. You could run Windows in a virtual machine, I suppose, but that would be of limited use.
You can install and run Microsoft Office in Linux, yes. You will need to install it separately, however; you can't just run the programs off your Windowspartition in Linux.
No. It wouldn't have any use even if it did.