My Q moved on herself ??

I just sow 3 fast moves on the screen.
Two from my opponent and my Q moving without my order !?
How it could happen ??

It cannot, you probably just mouseslipped.

again..

If you click on a piece and then click on another square that can make them jump, not just by dragging.

If you mean your Queen at home, women have their own strong minds, and will move without orders. haha :)