Downloading apps

Have you tried signing out of the App Store/iTunes, restarting the device, and then signing back in?

See the Apple Support article(s) below. 

Apps won’t downloaded. 

App Store, iTunes Store, or other Apple services - If you can't connect   

Some things you can try. Do you have access to another WiFi network where you can try? That has worked for several people.

Try a restart.

Restart your iPhone, iPad, or iPod touch         

Try a forced restart.

Reset Device.      

If necessary

Hard reset.        

Do a backup and try a factory reset. Then restore from your backup.

Restore to Factory setting.      

Restore - If you see an error when you update or restore your iPhone, iPad, or iPod

Backup - Restore your device from an iCloud or iTunes backup.