Why is my phone not want to download anything

See the Apple Support article(s) below. 

Apps won’t downloaded.  *

ASC YouTube for what to do if you can’t make a purchase on your iPhone -

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   *

Restart your iPad.   *

Try a forced restart. See the section towards the end of the article.

Reset Device. -

If necessary

Hard reset.     -

Do a backup and try a factory reset. Then restore from the 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.     *