Hi @MortenCopenhagen ,
Like @Dr_Shah_Imran , you are asking all the right questions, @MortenCopenhagen , and it is VERY clear that you are like me and Jan: eager to learn and motivated to do things correctly. So I am very happy to have these conversations with you because it is just great to find other Local Guide that takes our responsibility as Local Guides serious, in particular when it comes to Map Editing.
Your address answer is easy to answer and a perfect example where (IMHO) it is crazy where you have to look for it. Not on Local Guides, not even on the official Google Maps pages, but on Google My Business pages! Here is the link:
https://support.google.com/business/answer/3038177/#address
Make sure to click on the Learn More link, where you get all the important nuances!
"You mentioned we should use the Closed + Moved to a new location but you were not clear if it’s recommended to add the new address there when doing so. I expect we should. "
Your instinct is correct. Google Maps is getting a lot better in guiding the workflow. Thus, the new responsive edit forms guide us through all the desirable steps. This was very different in 2017 when I learned everything, so in a way map editing, is becoming a little easier.
So earlier the situation was: close a place and create a new place unless it is a claimed business where they have the “move option”.
Now the procedure is, close the place, give “moved” as the reason and answer the further questions of the responsive edit form. Today, they ask us for only for the address, tomorrow it might be different 
The most important thing to tell people (as it was also the case in 2017) is to NEVER change the address of the old location or move the Map Pointer.