Help! Can my parents see this on my iPhone!? 10 pts best answer [:?

[Molly]

Hi,
I just got the iPhone 5 and my parents have not yet received a bill with my new phone. I had a smartphone before, but it was a blackberry. I have a few questions about the way the phone works:
Does the data charge apply to third party applications such as twitter, facebook, instagram, snapchat, ...what about games like temple run?
Also, can my parents see which apps I have downloaded if they are not the 'credit card' holder on the app store account? For instance, if the 'data' bill is high, will the bill show, or can they easily get access to see what apps i have used and the time i've spent on them? Thanks.

By the way, I am on Verizon.