That's an unsolved problem. You'd be surprised how hard it is to separate certain parts from each other. But the first bulk sorting step usually takes care of picking out the larger assemblies and there is a class 'assembly' which gets picked out all by itself by the machine. That at least allows you to concentrate on the parts that are still stuck together.

Can the machine detect three identical plates stuck together? Just curious.

My most hated parts to separate are a flat dot on top of a regular dot. Second runner-up is the 1x1 plate on top of a dot, which is common in the Minecraft sets. I'd pay for a machine just to separate these for me!

Depending on the viewing angle: yes. If the part should land particularly unfavorably on the belt then there is a small chance that it would not be seen.