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I text on my iPod with an app, I was wondering if apps I've downloaded onto my iPhone would show up on my phone bill?

Nope.

My mother has been nosy lately, and I don't like her to read my texts, so I've started to use TextFree. Will she see that I've downloaded it?

Nope.

Also, does the web history show up? As far as I've researched, it doesn't, so I'm relieved..

You're correct in that web history doesn't show up, at least as far as I know.

And one more question... my mom said that the internet is "not unlimited", but we have wifi.. What does she mean? Like, as long as you have wifi, it's pretty unlimited, correct?

That all depends on your internet plan with your ISP. Some plans may include a specific amount of data usage, much like on your iPhone, where they will charge if you go over that allotted usage.
 
I text on my iPod with an app, I was wondering if apps I've downloaded onto my iPhone would show up on my phone bill?
My mother has been nosy lately, and I don't like her to read my texts, so I've started to use TextFree. Will she see that I've downloaded it?
Also, does the web history show up? As far as I've researched, it doesn't, so I'm relieved..
And one more question... my mom said that the internet is "not unlimited", but we have wifi.. What does she mean? Like, as long as you have wifi, it's pretty unlimited, correct? She's got me so confused. I only got my iPhone yesterday so I really don't know anything..
Thanks for reading xox

If she's paying for the phone and service, you really have no room to complain or expect privacy on "your" device. You can check what apps have been downloaded on the account history, and, again, if she's paying the bill the receipt will go to her. Data is "unlimited" if you're on wifi, but your cellular data depends on what plan you're on.
 
Thank you! Well there are 3 laptops used in my house, I'm sure there really isn't a limit or my mom would be on my brother and I's arses about it.

To clarify, if you're downloading apps using an Apple ID that has her credit card info and email address tied to it, she will be able to see the charge on her credit card statement and will receive an email identifying the app(s) downloaded.
 
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