Is it illegal, as it is in Germany, to claim that a crime has occured, despite you knowing that it is not true? Could Trump be charged with said crime?

In the US, yes. I believe it is called “falsifying a police report.”
Trump would have to file an official report and name names as to who he thought did it.

You can say whatever you please. If what you say damages me, I may sue you to recover compensation for the damage. But Trump is imune for anything he said simply through the claim that it occurred in the performance of his office.

He could be sued for slander, but those being named would have to bring the case. AND, they would have to open up all the books and allow both sides to see all the evidence. Something the Dems don’t want to do….ever.