Is it necessary for the mouse and keyboard to be on the same surface as the transmitter? I would like the transmitter to sit on the desk and the keyboard and mouse to sit on the sliding tray right under the desk.
is it necessary? No, not at all, you should be able to sit back and work any where with in your range.
I think it should be safe to assume that the device WAS designed to function a bit further than directly in front of the receiver, it MUST go further that wired or its redundant. we wouldnt see the need to buy their new products if it would only benefit battery manufacturers and micro$haft.
how keyboard work as transmitter.
no, you should be fine