How to stop checking for mail and asking for backups?

My mom is using Android 6.0.1. The problem she was having last week was that her phone was checking and downloading her email, and she did not want that. So I signed her out of her Google account, which fixed the email problem but created a new one. Now the phone is spawning messages that her phone is not being backed up (presumably because she is now signed out of her Google account). She does not like those messages either. What is the best solution to this problem? I.e. stop the emails without disabling other phone features. Thanks. Galaxy J3 Luna Pro