Causes for drastic change in battery drain on a Logitech wireless keyboard

I'm going to answer no - it is not possible. There appear to be similar questions on Logitech's site so you can search there as well. I suspect the answer is that when you pair, the transceiver and the device exchange several bytes of random data and form a key to both allows the devices to recognize each other and to encrypt their wireless transmission.

The problem is that the transceiver may have the ability to recognize something like 5 devices, but the input devices can only recognize and pair to one transceiver. That's because the transceiver only has to sit there and accept a signal it recognizes, otherwise it is passive. Sit, if you see a signal with the correct encryption and ID, accept input, otherwise ignore.

If you added the ability to have the input devices (mouse, keyboard...) pair to multiple transceivers, you would require some sort of additional buttons on the device to switch between them. You'd also need to have the input device store the state (caps lock, num lock...) it was in for each transceiver.

The only Logitech device that can do this is the new K760 keyboard for bluetooth. None of the Unify devices appear able to do this.

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.