I may have chosen the wrong software, if so, sorry!
The question is in the title... Is there a way to make icons on the desktop between activities totally separate?

One possibility is to create a directory (for example, a hidden one) for each activity, place icons you wish into each of them and set up the desktop for each activity to show that directory instead of HOME.

Sounds like a good idea... How does one assign different directory to an activity?

When you switch to an activity, right-click on the desktop -> Configure Desktop -> open Location tab and choose a specific directory to show instead of the default 'Desktop folder'

Thanks!