Your data are clearly not normally distributed, so you should use statistical methods taking that into account. Many textbooks and articles are available on this subject.

C.A. (Kees) Kan

Of course, I know.

But my question was not wich test to use but what should I do with values below the analytical threshold. I have to manage them in somehow, because they are senseless (negative concentrations).

There are several options as you mentioned. There are pro's and con's to all. The main thing for me would be to clearly state how you treated the data, to allow readers to value your results based on their experience or preference.

I am a bit surprised by the non detectables. I would expect that modern analytical techniques like ICP MS, would detect heavy metals (due to their wise spread presence) in all environmental/biological samples.