Secured Wi-Fi usage and what they can see?

I work for a 911 dispatch center in a small county and access their secure Wi-Fi with a password. I have an iPhone 4S and was wondering what all they can see as far as what sights I visit on safari and if they can see what downloaded apps I access that I have downloaded from the App Store.

Yes, they can if they wish to log that information. Considering this is a 911 center, I suspect EVERYTHING is logged, including all network traffic…

  • Under settings on my iPhone, does the data usage include Wi-Fi usage? Because its stating a ridiculous amount and I've had my data off… And my Wi-Fi on. Does the total of data include the amount of Internet I'm using when on Wi-Fi? I'm so confused
  • Somebody has accessed my secured WPA home network with no password whatsoever? Two nephews at home… One needed the password, one could access my very own home network with no password whatsoever, and did so on another network. What sorcery is in his iPhone? I'm very worried. Again, it seems he can access networks ignoring their security, happened at least twice, not just my own network.
  • IPhone: settings cell usage vs AT&T's data usage number? AT&T has a number, by calling it will send you a text message telling you how much usage you have used on your data. But also in the iPhone there's a cellular usage count in the settings app which also tells how much data you have used. Both of my cellular usage counts are different. Which is right?
  • If you had a time machine and could see 1 person, who would you go see and why? I would see Aristotle, not only would I be able to bump shoulders with Alexander the Great I would love to pick at Aristotle's brain about philosophy, his views on life what he thinks the meaning is and how he sees the world in a few thousand years, maybe even slip an iPhone in his pocket and see if we have flying cars and floating houses when I come back to the present.