As a newbee I tried to add a tabletop to the template puppet "Dave", in a way that this tabletop is completely independant from the puppet, but both hands should be on top of the tabletop. Right now the table is moved around if the right arm is moved. How can I unlink the table from the hand/arm?
You are doing the right sort of thing putting the table in the middle of the hierarchy, to get half the puppet in front and half behind.
Well, actually, if you only have the chest of the puppet there is another option. You can nail down the desk with pins plus putting sticks along the straight edges of the table. Then the table will not move. You don’t need it independent - the desk effectively becomes the bottom half of the puppet which is pinned and sticked to stop movement.
If however you want the puppet to move around behind the table (sway from side to side, stand up, etc) then you need To do more like what you are doing. To stop (or reduce) movement, you would say pin down the feet of the puppet character so something is solid and unmoving. Then move the origin of the desk to the same point. At the moment the origin of the desk is near the middle of the desk, which means it will move with that point on the parent puppet. So just moving the desk origin point should help reduce movement. The other one is the attach method (free, hinge, weld). You could try “free” to see if that helps, hinge otherwise. Weld it will sway more with the puppet body.
There was another recent thread with exactly the same discussion. I will try to find it as well.