edit: I have some questions
one, about how long does the battery last? three times. not doing anything, using a small app (like Kindle), and using a more demanding app (like radio, Skype, or Steam [assuming these are demanding])
also, how much data do they use? radio, Steam, and maybe BLF with Safari?
is there a way to check what apps are downloaded? will my mom be able to see if I get an app, then delete it?
i can answer one and three, no two because i use an iPod touch and both devices have the same battery
1: most of my stuff uses internet, so my iPod lasts me around 10 hours depending whether i do it all in one go or slightly less if i spread the time out. Also using wifi and 3g will drain your battery quicker turn it off when your not using it.
3: your mother can check downloaded apps, but not delete them unless she has your iPhone or its plugged into her laptop and she knows your apple id password.
hope it helped