First off, welcome to AO

1) Probably your best bet is Process Explorer. Its a handy little app that will allow you to view all the threads currently running on your machine, as well as connections made by those processes.

2) This doesn't really seem like a question, but rather a request to be taught about security. As a relative newb myself, my advice is to read as much as you can, and try to get a machine on your network specifically for the purpose of learning the ins and outs of the O/S, software, etc. Don't expect anyone to spoon-feed you all the answers.

3) This is pretty much based on two things: Personal opinion, and relative skill levels. Generally, Linux is viewed as being somewhat more secure "out of the box" than Windows, but on the other hand, Windows CAN be just as secure in the right hands. I recommend a dual or multiboot with Windows and at least one distribution of Linux, and learn about both - it will hold you in good stead.

4) What method did you use? It sounds like the command "tracert", but that's a really round-about way of getting your local address. If your computer connects directly to the Internet via a modem, use the command "ping". If you have a router connecting to the modem, check your router's status - most half decent routers will show you your "public" address, as well as any DNS servers you are allowed to use.

Good luck!