Putting apps from itunes to iphone?

Someone messed with my phone and itunes and the apple store were missing along with 3 other apps. I went on itunes to get them back and could not sync them on my phone, so I restored my phone and afterward was left with no apps except the ones that can't be deleted (I still didn't have itunes or the apple store. I tried taking the apps that are on itunes and put them on my iphone but it won't work and i'm not sure why

Added (1). On itunes because i don't have the app store on my phone anymore

You can just redownload them from app store for free. Say one of your apps was fruit ninja, you can just search it, then redownload it.

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