So, it happened that I tried again and the dishwasher was able to perform two cycles without problems, the first was a quick one, the second was the all-inclusive powerscrub strong steam extra rinse.
However, the machine emits some "grinding" noise that is relatively loud. I recorded it and you can hear it in the following video; do you think I should get ready and buy some replacement for when the dishwasher will have "eaten" all its gears
Also, can you give me an advice where the little hose in the pictures should go? My small kid pulled it out from somewhere... over the course of a washing cycle it spits out some water...