So in the last week, I've gotten a few friend requests and realized that an email was never sent to what email address I have listed on my account settings. I checked the 'junk' folder too and nothing showing. Any idea if the emails are being sent when we've got the settings checked to be notified of the various things in the account settings?

Emails appear to be working properly. It's always possible that an email could be dropped / lost in transit, but that should be very uncommon.