Airport on iMac 10.5.8

I have recently started to access the Internet using the Airport facility on my iMac 10.5.8. When it scans for available modems there are up to 4 other modems in the vicinity. One of those modems, called dlink, is not locked, as all the others are. My modem is my iPhone. I have noticed that after I have closed my iPhone modem down and gone away from my computer for a while, when I come back my iPhone modem has mysteriously been turned back on and the Airport is connected to the dlink modem. When I go into Airport it says that it is connected to dlink. I am concerned that dlink is in my computer. I phoned a tech who didn't have much time to talk but he said that it could be possible that dlink is in my computer doing God knows what. But then he asked me about sharing. I checked the set up and was so grateful to see that when I first set it all up I did not have any software, or otherwise, checked to allow sharing. The tech then said that I could possibly be confident that dlink was not able to get into my computer. I am wondering if dlink can get in to my computer. I would also like to know how far away these other modems can be before my Airport cannot detect them. I've also noticed that as soon as the Airport scans for modems it connects immediately to dlink. I have password protected my computer so that after 5 minutes of inactivity it goes to sleep and requires the password to be entered before logging in. I have also decided to turn Airport off whenever I am not using the Internet but have noticed that it is very easy to turn it back on as there is no password to turn on so that turning Airport on or off is password protected. How safe is my computer against the likes of dlink who leave their modem unlocked and turned on 24/7? How easy is it for others such as dlink to get in? What do I have to do to prevent them getting in? If I am logged in to my computer and on the Internet is dlink able to get in and get my passwords and things like that? Thank you all