> Interaction menu: It seems that the contents menu is also called interaction menu sometimes.

That's completely Zapper's fault for breaking naming schemes!!!

> Every time I use it the GUI completely blocks everything on screen. I would like to see what is going on.

The game doesn't tell you (*cough*) but there is a minimise button in the lower right of the menu. Of course, you can't access everything from the minimised menu but maximising is no problem!

> Digging & Hangling

Yes, it seems we have to do something about those actions. I guess the 'why' it is like that is obvious, it somehow fits the animations and was a try to be more realistic. But gameplay-wise it is true that slowing down your character for no good reason, even making it less nimble(!), is a bad idea.

> Chopping & Digging

I'm reluctant to have anything lock the clonk in a certain state (like click at x,y and the clonks digs until there or click tree and the clonks chops until chopped). Not only is this error-prone (stucking permanently in a certain state) but it is a slight contradiction to your previous issue: not having full control over the clonk at all times. You'd need some kind of cancel button.
Games with a similar control scheme than clonk (to my knowledge) also don't seem to take this path. In Terraria / Minecraft, you also have to hold down the mouse button to mine / chop trees