Should I (in order to preserve battery life) turn off the Bluetooth mouse at night? Or does it not consume any significant amount of power when it is not being kicked around anyway? Or maybe goes to sleep by itself after some time?
Turn it off. Save a lump or coal. Bluetooth drains a decent bit of power, on a mouse, not much, but assuming your leaving it off for 12 hours instead of being on for 24, your doubling the battery life.
As per it going to sleep, some do, some don't. My bluetooth headset does, my former mouse, did not.
This green energy tip brought to you by a prius driving snob. :)