How does the fan in the jet engine suck in air while the engine is stationary?
The answer in all cases is the fan accelerates air, creating a low-pressure area, and more air moves in to fill the low pressure.

Consider a ceiling fan.  As it runs, the air in the disk of the fan is accelerated downwards.  This means that the space where that air used to be is now at lower pressure, since some of the air has been removed from it. Air below the fan is moving downwards, away from the fan, so it's difficult for it to fill the low-pressure zone. So the air that moves in will come from the top and the sides.

If you put the fan inside a tube (a duct), the air can't come in from the sides, so it must come from above.  You now have something conceptually similar to a vertically mounted jet engine, except that it's much simpler (actual jet engines have multiple fans) and it's powered by a little electric motor, rather than by injecting and burning fuel.

If you want a pump, the fan doesn't care if you put in a false ceiling that divides the space above the fan from the space below it, with the duct and the fan as the only connection between the two.  Since no air can get into the area above the fan, the fan will pump the air out of that zone.  Eventually, the pressure in above the fan will get so low that air the fan is accelerating downwards will start to flow back up into the evacuated zone.  This is why any particular fan will only lower the pressure by a certain amount.