Adv. Outreaches: Publish should be renamed to run now or show a popup

YES. This was something that I was confused about. I (luckily) clicked it about 30 mins before the AO was going to run anyway, but it was still confusing. That verbiage would be super helpful!

Also, a better way to schedule it in general would be nice. How do you turn it on then outside of "Publishing" at the exact time you want it to first kick off?

Seconded!

Additionally (and I may post a separate thread for this if needed) - Email Assist should also have a popup to confirm that the sender is ready to send the email/outreach.

It's preferred that ANY communication sending action has that final, "are you sure?" popup. 

Hi All,
Thanks for reaching out, There is a big difference between how AO versus email assist and outreaches. AO is a workflow engine and once it is published it means workflow is published, and will start processing only on Run Date. Now as soon as participants get added they start processing, hence its important that participant adding schedule should be set right in order to trigger email at right time.
Each and every participant is executed independently as they can be in different stages during workflow, this is different in Outreach and email assist where its bulk process.