Because it's a race car.
All race cars are mostly going for the weight so they remove the starter and instead have a manual starter that they have in their hands, start the engine and remove it.
Simple
And some cars needs to be pushed to start (not many).
Yes, but tehy were hugely impracticle. There wasn't a quarantee that you even could start it up again... and there was not enough power to try it twice.
Nowdays it's impossible to stall an F1 car with all them technologies