Yes, but it will not start again without electricity. alternators only provide electricity when the car is running, they're of no help when the engine needs to be started.
no
Railroad trains have - and continue to - run on any of three powers: Coal (steam), diesel fuel, and electricity.
motorcycles use a magnet system to generate electricity for the spark plugs they cannot run without electricity because you need electricity to ignite the gasoline but they can run with no battery if you have a kickstart or you can bump start them
An older, completely mechanically controlled diesel engine could, provided it had electricity to start it. A gasoline car could not, as electricity is required for the spark plugs to ignite the fuel in the cylinder.
Yes the engine can run without the power steering belt, but would be very hard if not impossible to steer around a corner. Even if the belt were a serpentine belt driving the Power Steering Pump, Alternator, and Water Pump the car would continue to run until it overheated or ran out of enough electricity to run. However if the engine was an OHC engine and the Cam belt breaks it will stop running.
of course
A 306 HDI may continue to run after you switch off the engine if the ignition timing is set improperly. This will force the engine to continue running for several seconds.
You can run an engine in/out of a car without a transmission. Car wont move and engine wont be mounted properly. So i suggest not to run an engine without a transmission unless you know what you are doing.
The engine should continue to run... if and only if the alternator is putting out enough electricity to keep the onboard computer and other necessary electrical engine parts up and running.
With a blown head gasket the engine will still run, poorly with issues, but run. A blown engine will not continue to run from that moment on.
they are thermostaticly run.