1. Because you didnt know the answer to question #3
2. Its online 24/7*
3. Yes
*
, has better internet speeds and it is dedicated to running what you want it to run. You use your pc for browsing, playing games and so on. That will slow down the server and if you download things the ping will most likely go crazy. Plus, power isnt free, so you would probably turn off the pc wich means the server is offline until you boot it up and start it again.
In regards to question #1:
http://en.wikipedia.org/wiki/Port_forwarding
In regards to number 2:

(Hosting provider I can vouche for)
In regards to #3: Look at number one.