I don't see why not. Most servers used in Dedicated Server facilities are made with off the shelf desktop PC parts, not servers or server grade equipment.
You're going to need to contact your ISP if you want to try and run a server from your home. A residential ISP account will not cut it, and nearly all of them forbid running servers in their AUP. You'll need to look at getting an upgrade to a business class line, ISDN or T1 with as much upload speed as you can afford. Plan on spending $100+ for such a line.
Sure you can, but analyze first if it's worthy of your time and effort. Most of hosting companies have specially designed servers for this purpose and super high speed optical fiber internet connection + the whole mass of other technical stuff to maintain the network. So it's hard to create anything that could compare with professional hosting. But of course it depends what is the purpose of doing that in your case, if it for example for learning server administration then it's a very good idea.
First setup is make sure your internet connection can handle it plus will your ISP allow it. If you are just hosting a small site it should be alright if traffic picks up its going to bog down.
yes, but your site speed will be limited by your upload speed set by your ISP (1MBs for cable? vs 10MBs or 100MBs of the hosted server)
don't do it from home. once you get some more simultaneous connections you won't be able to use your broadband and you will be facing a serious speed issues with people accessing your site but think about colocation instead (I mean if it's a machine you're not using)
Yes. You can install apache server which allows you to serve up web pages and access your machine.. Once it has been installed, the security holes are to be hardened.You can get the complete details of the server configurations and the installations from http://outsourceservers.com/server-setup.php