Possible to capture all the tcp packages sent from my computer?

Hello guys,

I am interested in writing a little tool to capture all the tcpip packages sent by my web browsers (multiple browsers). I heard that every request sent by a browser actually uses a different port. So is it possible to write a program using QT to listen to all the ports?

Suppose I have two applications that are listening to the same port. Can both of them respond to the tcpip request? Or the operating system will only give the package to one of the listeners?

I know a tool called TCPView for windows that does this. But since I am using a different operating system and there is no fun to use a readymade tool, I still want to write one myself.

Thanks,