You are turning the first motion shaft of the gearbox ,pressing the clutch deactivates this probably is about 1% power saving.

yes. less drag from the gearbox. May well be marginal but if a battery is on it's last legs it helps

Unless the clutch thrust bearing is noisy (whines when you press the clutch) or the crankshaft thrust bearings are very worn (engine stalls when you press the clutch)

But with these very low temperatures with the gearbox oil being very thick due to the cold if your battery is a bit flat and if the car doesn't have the above problems pressing the clutch in may well make the difference between starting and not. As previously advised.

Also the first thing to do if you think the battery may be a bit marginal is to turn off everything electrical that you can before you turn the key. If you've stalled and the lights are on then turn them off before trying to restart if its safe to do so.

New Astra the same the engine will not turn over until you depress the clutch pedal,I seem to remember Saab and possibly Audi use the same system