Bartek,
> Can I glue the plywood in place where the wall is and make the trap more movable. <
Yes, absolutely.
> how important can be the thickness of this back wall and how steady does the trap have to be mounted to the wall <
The back needs to be rigid enough not to flex. If you use at least 3/4 inch plywood, MDF, or particle board, it should work okay. It does not have to be mounted securely to the wall, but it must rest against the wall. Wood panel traps do not work well when spaced out from the wall. So make sure the back is right up against the wall.
> can i just lay the trap made that way anywhere I want,like just lay it on the floor by the wall? <
Again, it must be right up against the wall. And bass traps always work best near the corners. So you can lay them on the floor horizontally, but they should be against the wall and parallel to it. The corner between a wall and the floor, or the wall and the ceiling, is just as valid as a regular wall/wall corner.
> 4 inches is 10 centimeters,which I can't find. They have 9 centimeters. 2 inches is 5 cm.,they have either 4 or 6cm...etc. <
Small changes like that are okay. If you increase the box depth the center frequency shifts down a little. So as long as the change is no more than 10-20 percent you'll be fine.
--Ethan