If I took out my Daugther from family sharing why she can't get in her apple store and download anything?

When the App Store is disabled, there is an issue with the App Store and iTunes account, which will require you to contact iTunes Support. In order for your daughter to download apps, even free ones, as long as they offer In-App purchases she will need to have a valid payment method tied to the account.

Why, did you remove a 16 year old from Family Sharing? If she doesn't have a credit card (not many 16 years old have their own credit card), you have made it more difficult for her.

Click this link to see how to contact iTunes Support --> If you see a message that says 'Your account has been disabled in the App Store and iTunes' - Apple Support

Does she have her own Apple ID?

Does she have a payment method set up under her ID?