Hello,
Finally it seems root cause of the issue my four mosfets were broken, all of them.
I don't understand why this happened because I only tested with some milliamps.
Now I used brand new and I cannot see previous strange square signals.
Thank you very much everybody's help!
Anyway, I attached measurement with the good mostfet (STD16N65M5).
I marked with green two points on the blue measurement. Maybe this is indicating parasitic coupling?