Help with Internet Help

My g/f has a Toshiba A-135. The darn thing seems to constantly pop up with this internet connection window called "Trendmicro PC-CILLIN Internet Security 2007" then lists IP addresses of Computers who are connected to her personal network. Then asking to "trust" or "Do no trust", and always selecting 'do not trust'. I have set up the network to where you can only get onto the internet with a password. I do have a couple questions:

1. If there is a password requirement(I have had to enter it with my own laptop at her house), why are these people allowed to get on her network?

2. Are the individuals actually connecting to the network? or is it just showing who is trying to attempt to?

3. Is there a way that they are connecting to her actual laptop?

4. How can we stop this annoying program from popping up every 5 min.?

Any help would be great. Thanks.

 

I would just uninstall PC cillin. (unless you paid for it) - I've been using built windows firewall with no problem.

 

i take it then that the program has nothing to do with the laptops ability to connect to the internet? if not then i will go ahead and remove the program. thanks