Can I set up Linux on a Mobo with WiFi to serve as a Server and Wireless Router for my home?

Yep, search for 'linux router project'
There are several tiny distributions the will do the job for you. I've used ones that fit on a floppy disk (ie no HDD required at all) that would lend themselves quite well to running off a flash memory device much like modern home routers do.

According to Wikipedia, The Linux Router project has been defunct since 2003.

What about LEAF? Is Zebra an option for wireless routing to the Internet? And, would I still be able to run the same computer as a server and router?

You should definitely look at the DD-WRT project or at OpenWRT - both of these are embedded linux distributions that are designed to install onto a standard wireless router such as a linksys wrt54g, but they can also be installed on a regular computer.