Can a Microsoft Mouse and Keyboard share the same Nano Transceiver

I too had this same problem with my 3000 keyboard, because the transmitter is a nano transmitter there is no resyn capability (no mouse with this keyboard...the keyboard IS available without the mouse combo).

I contacted Microsoft and explained the situation and seeing as the keyboard has a 3 year warranty, they replaced it right there & then, no questions asked. all I had to do was supply them with the model#, serial# and where I purchased the item from. I was pleasantly surprised.

while I am using wireless mouse and "not using" wireless keyboard, is the latter discharging its power count-downing its life-time?

Short answer, yes.

Is it possible to switch off the keyboard (or mouse) without removing batteries?

That depends completely on the device specifications. Some devices the only way to turn their power off is to remove the batteries.

Will it be enough just to isolate battery contacts?

As long as the batteries are separated from the battery contacts, such as using a thin piece of plastic like stores use for devices that come with batteries, then you should be fine.