</font><font color="blue" class="small">( If I log on, can they tell I am on? Would it affect the performance of the system for them? Could they see what I'm doing? )</font>
Technically, if you can receive the signals, you can do with them as you wish. And, some would argue that if your neighbor chooses to leave his network wide open, unencrypted and insecure, then he/she is inviting others to connect. Realistically, it's probably just a user that doesn't know any better. The noble thing to do would be to let your neighbor know that you can access his/her network and see if they mind you using it. If they have a broadband internet connection, you may even approach them about sharing the cost of the internet connection. The less than noble thing to do would be to mooch bandwidth off of them without them knowing. /forums/images/graemlins/laugh.gif
To answer your questions, with most wireless routers, you can see how many clients are connected, so yes they would be able to tell if you were connected or not. However, most home users probably never look at their router diagnostics as long as everything appears to be working properly. But, you may have a paranoid neighbor that keeps a constant watch over their network. You never know.
It wouldn't likely affect the performance of their system any significant amount, unless you were pulling down big multimedia files all the time.
Technically, they could "see" what you were doing by intercepting/analysing the packets before they get to you. But, again, most home users aren't going to be tech savvy enough to do this. But, again, you may be lucky and have the paranoid geek for a neighbor. They may have set the "free" network up as a "honeypot" to trap unsuspecting moochers. /forums/images/graemlins/laugh.gif
If it were me, I'd casually bring it up in conversation and see if they mind you making use of it. And, as I said before, maybe split the cost of broadband with them in exchange for the use of the wifi signal.
BR