How do I edit the url of an existing post or define a url before a post is published?
Not within Discourse. The URL is defined automatically/dynamically, and will always be: http(s)://yourdomainhere.tld/t/topic-title-here/topic-id-here
How deep is that logic, can it be modified without breaking the instance?
I’m honestly not 100% sure. Educated guess, it would be incredibly complicated to write a plugin that would modify the URL logic.
Admins can do that in WodPress, so I was hoping that Admins in Discourse could as well.
Actually, the topic title in the URL doesn’t matter. You can put any text there. Only the topic id matters.
What are you trying to accomplish?
True, but putting Can an Admin editing URLs? into the address bar will automatically resolve (and be displayed as) Can an Admin editing URLs?.
Easy to remember urls for groups
Check out permalink in customizations.