Thanks for those very nice questions!

I must say I already learned something new in the first two lines. What kind of material is being used in such detectors and how do we explain the fact that dark matter particles only interact with the detector material once in a while?

Dark matter must be very weakly interacting with the Standard Model. Therefore, it must be very weakly interacting with normal matter (made of standard model particles). However, "very weakly" does not mean "not interacting". The interactions are super rare, but they happen. By constructing a super large detector, we hence multiply the chance to have such interactions.

The best current choices are detectors mande of xenon gas. You can for instance see here. The xenon-1T (1T stands for 1 ton) experiment has recently released its new results.

So they basically estimate the dark matter interaction relatively to the dark matter mass? Is that hiw dark matter models are created?

It works both ways. By the size of the limits for a given mass, we can have some idea about what makes a model viable. In the other way round, when starting from a model, we can predict the production rate. `the main dependence of the production rate comes from the dark matter mass, which explain the chosen representation for the results.

Is it clearer? :)