Yes, I bought this two weeks ago and just had to open the box and plug it in!
No, it does not have a thermostat control.
No, it is not recommended to be mounted on the wall.
It is not on wheels. It is just a flat bottom "wooden" box.
The item is 7.50 inches in Depth
It measures 7.50 in (D) x 23.00 in (W) x 22.75 in (H).