@Probably, by the looks of it, you are in for a lot of primary research, though, I'd suggest you consider flipping it upside down, for the following reasons:
I would like to make a poll with questions like "What emotions do you
associate with the word "ka:men"?" and compare whether these answers
are closer to the true representation of the word rather than answers
to the questions like "Which of these objects would you guess "ka:men"
to represent?".
You might have a hard time collecting a sufficiently large number of responses to validate your analysis. However, you could turn this around and look at how various languages express certain primitive / instinctive emotions. This wiki entry: https://en.wikipedia.org/wiki/Cross-linguistic_onomatopoeias has a fair amount of reliable data both for emotions and for things that have characteristic sounds - these could serve as a reference point for both theories as well as a pretty solid ground for your research hypothesis.
This is by no means supposed to imply not to conduct your experiment, but it might be a lot more tricky to conduct than you think. A fascinating read that would also be appropriate for the second half of your questions would be: https://books.google.hu/books?id=oEO0BQAAQBAJ
Even if you do not have the time to read it cover to cover, its overview of language origin theories would be a solid background. The experiment design sections may also be beneficial for your own poll setup.
