I have a wifi antenna. There's a bunch of free wifi around but there is only one area of my house that can access it. Can I use the antenna and set up a router using the existing wifi. To "repeat" the signal?
The answer for that would be "potentially yes". Easiest way I know of to do it would be to get yourself a cheap Linksys WRT54GL, flash the firmware to DD-WRT, and then set it up as a Repeater or Repeater Bridge. There are plenty of tutorials out on the web on how to do this. Your antenna may or may not work with a WRT54GL, so you'll need to research the connectors before you go chunk down your money. The gray area comes into play with the legality of the issue. Are you going to be using an open AP with the owner's knowledge and consent? If not then you could be in for a world of legal issues, and my advice would be to not risk it.
Yes it's possible to use some routers as repeaters, for example the Linksys WRT54GL: http://lifehacker.com/265142/turn-your-wifi-router-into-a-repeater