No, many of them had electric pumps, even relatively old cars had electric pumps.
You think that all of the fuel in the float chamber evaporates overnight?
If you run the float chamber dry on a car with a carburettor it takes a lot of cranking to start the engine. What remains in the carburettor enables a relatively easy start.
Yes, I think you may be thinking along rails.
So you reckon that starter cartridges didn't work them?
Note that I pointed out that you need to get a fuel-air mix into the cylinder and to close exhaust and inlet valves to get it to work. It's not beyond the wit of man to do that mechanically or with simple electrical systems. On a diesel engine (working in the other direction) there are decompressors to allow easy starting. When the engine starts to turn over the decrompressor disengages. The same mechanical mechanism could be used to close the inlet and outlet valves instead of keeping them open and then revert to cam operation when the engine starts to turn over. Fuel/air could be injected using a mechanical pump and that (mechanical) system has been available for a long time.