invalid emails keep popping in and out of inbox

Looks like you have got on the end of some sort of spam / phishing email list. I would suggest to setup a rule to automatically move those type of emails to the spam folder or rubbish bin folder.

You can “Right Click” on the (Senders email address) at the top of the email and click “Create Rule From” at the bottom of the menu that appears.

Then click on the word “Folder” at the bottom and select either “Junk Email or Trash” folder in the browse window and then click ok. Next click “Next” at the bottom till you get to the end.

That should then automatically move those emails to either the Junk Email or Trash folder which ever one you chose when they come in again.