I have been trying to send an approved email draft to my personal email for review for the past few days, and have yet to have a successful attempt. Can someone please look into this?
If you could post a screenshot, it could help us troubleshoot.
You need to ensure that there is an address that does not filter emails, otherwise you will go around and around trying to see if the email was correctly assembled and routed at the basic SMTP level.
I don't advise whitelisting Marketo email: this will merely disguise real-world deliverability problems. But you must have a way to verify that emails are going out. Have your IT create an unfiltered mailbox for you.
Then maybe the best is to first verify your instance setup, especially email deliverability: Setup Steps - Marketo Docs - Product Documentation