Belt sometimes goes off under the rain

Thank you for the explanations Chris.

I had to turn myself into a beast to loosen the freewheel.
But that’s done, I succeed.

Here are photos.

3 questions :

1. On the freewheel, I notice there is a gap beetween the ring and the edge :

Maybe it explains that the belt is not centered as it should be.

2. In the wheel itself, I noticed a part which is free to move. Is it normal ?

3. Is it required to tighten the new freewheel as high as the previous one ?

I would say no.