The subwoofer is a speaker that points to the ground. It's purpose is to provide non-directional bass sound. It gives you that "thud" when there are explosions for example. The subwoofer only reaches its full potential by being placed on the ground in it's correct position. If you put it on a shelf more than likely you are going to get a rattling sound due to the vibration (unless the furniture is really sturdy). And I would not recommend placing it on it's side at all. It wasn't designed to be operated like that.
It's not wireless, it's big and ALL cabling has to go through it since the amplifier is built into the subwoofer. The cabling to the soundbar is pretty short (and proprietary) about 10 ft, so it needs to be close to the TV instead of being places somewhere unobtrusive.