Four questions about usability in Spaces in Catalina

While there is no way to change desktop names without jumping through hoops, there is something you can easily do that will help you set them apart: add a different desktop picture to each desktop. You can even, if so inclined, use a picture that includes your intended use of the desktop - like "Play" or "Work".

1) No.

2) You don't really "set up" a Desktop. You can assign apps to a particular Desktop, but if you move some of that app's document windows to a different Desktop, they won't reappear there when you open them again. Documents are not assigned to a Desktop, only Applications.

Also, Full Screen apps get their own Desktop. That Desktop will appear in sequential order from when the app was sent to Full Screen.

3) No.

4) Yes, ctrl-click on the desktop icon and use the Options submenu to assign it to a Desktop.

You have your monitors set up to allow apps to span across the two, simulating a single display. There is no way to set up Mission Control to assign a app to a particular location on the Desktop, but the App will remember its location.