When I place a few objects one over another, each with different colors and transparencies, so that they all overlap somewhere, how would I measure the color on this overlapping area? Similar to the way the eyedropper in photoshop would just give me the color of the pixel he is hovering.
Is this possible without ridiculous detours? All I could imagine is making a screenshot pasting it and measuring from there - but this kind of the definition of a ridiculous detour...
Another slightly easier workaround would be to use Photoshop's eyedropper tool directly.
This doesn't seem to be commonly known, but it can sample outside Photoshop docs.
With the Eyedropper tool selected, click and hold in a Photoshop document, then drag to any point on your screen, release and you'll sample the colour at that point.
I think the closest to what you are looking for is Flatten Transparency, under the Object menu, which breaks the selected objects up into objects with fill colours based on the result of their overlaps. Still a bit of a detour but it gives you the colours as proper fill colours which can be picked up with the eye dropper or used any other way.
Since it changes the original objects you'll probably want to copy them off the art board then flatten transparency the copy, or, flatten, get the swatches you need, then undo the flattening.
(when working in cmyk, watch out for gamut-related surprises when turning the partially transparent version of a red or blue into a solid swatch, resulting in what appears like a big change in colour)