Emojis appear on some parts of apps but show as question mark in other parts
I had to reinstall Mac OS. I did this by pressing Command+R on reboot and then it present a menu. You chose Reinstall Mac OS and it'll reinstall it for you.

I did a backup before doing this reinstall using TimeMachine and an external drive because I thought I was going to have to restore everything again.

Good news is that I didn't have to at all. All my files were intact and the emoji issue was fixed! 

Here's more info on this type of install.