Issues sending sample emails to myself for testing

Marketo sets priority for all different actions. Here's a good summary (albeit from 2016) to get an idea about that.

Hours for an email send are definitely not normal and could justify further exploration or support tickets. Campaign membership, though, is definitely lower on the list of priority—and for good reason. I've seen a number of people lately asking about campaign members not showing up, or activity tracking not appearing on a person's activity log, but the question usually gets back to whether or not the action was happening vs whether or not the log was being updated; and in most every case, the activity happens the log just isn't updated (because it's doing more important things first). 

A good thing to do is the normal log out/back in, refresh cache and all that stuff; but also check your Campaign Queue to make sure your instance isn't running through a lot of actions at the time.

If nothing seems to add up, it might be worth having Support clear the cache on your instance just to make sure there's nothing stuck somewhere; and obviously if that doesn't solve it they can open a ticket for you as well.