Questions about Airport Express?

I learned that it can "extend the range"

The AirPort Express can extend the range only if there is another Apple router providing the wireless signal.

and there's an unsecured network close by, and it's not very close, so would it be possible for me to extend it to my area?

Only if the network is provided by another Apple router.....and....that router has specifically been configured to "allow" the network to be extended by another device. Unfortunately, the chances of both of these things being true are very unlikely.

To avoid these obstacles, I can create a new network WITHOUT accosiation with my home's main wifi to prevent the 12 am timer?

Sorry, but that is not possible unless you have your own Internet connection and modem.

And I'm interested in using my iPad as a PC replacement (I have a crap 2004 PC from my step dad), by using iWork apps and wirelessly printing Pages instead of Word.

That would be a question that you need to ask in the iPad Support Community Area.

Using iPad