Currently active abilities are only visible above units, which is very chaotic with lots of them around and they also disappear when the cursor is not nearby, and to the left of the portrait of one of the selected units.

Could all abilities of all selected units be added to a static overview(not moving across the screen like the icons above units) that functions like the ability next to the portrait so it is easier to manage?

it's already quite easy to manage, Blizzard style:  Have a group of mixed units, press TAB to cycle between them.

You then can choose to press Y, X, C for the 1-3 abilites, or TAB to cycle again.

This is technically not feasible, I'll be moving this to rejected.