it depends on the design of the pump - centrifugal pumps tend to like water cooling their seal surfaces, unless they are specifically designed to pump air as well as water. Positive displacement pumps also typically use the pumped liquid as thier sealing surface cooling. Both can be designed such that cooling is provided externally, and pump air as well as water (there are both kinds used as air compressors). A typical submersible pump would not pump air very long - minutes to hours at best.
It wouldnt last long as the water acts as a lubricant and the seals would fail as a result .The bearings would also overheat if relying on being cooled by the water
It depends on the type of pump.Some pumps can others will burn out. Carpet cleaner type suction will happily cope with both air and water,old fashioned hand operated lift pumps do as well. Bilge pumps etc do not like running dry and will have to be reprimed to suck water if the get an air lock.
# Water pumps are generally centrifugal pumps except few specific applications. #Centrifugal pump will not pump,untill and unless the the pump is properly primed [atleast ,casing upto impeller top should be fully submerged with water.] #Since the weight of water is approximately 8000 times that of air (50 miles vs. 34 feet or 80 Km. vs. 10 meters) the centrifugal pump can produce only 1/8000 of its rated liquid pressure. In other words, for every one foot water has to be raised to prime the pump, the centrifugal pump must produce a discharge head of approximately 8000 feet (each meter requires a head of 8000 meters) and that is impossible with conventional impeller diameters and speeds. *All of this means that if you intend to use a centrifugal pump you're going to have to come up with some sensible method of priming it. Your choices will include : *Install a foot valve in the suction piping to insure the liquid will not drain from the pump casing and suction piping when the pump stops. Keep in mind that these valves have a nasty habit of leaking. *Evacuate the air in the system with a positive displacement priming pump operating between the pump and a closed discharge valve. *Fill the pump with liquid prior to starting it. *Convert the application to a self priming pump that maintains a reservoir of liquid at its suction. # Also it is advisable to prime the positive displacement pump to run the pump smoothly, as if for some time it is pumping air,there will not be force balance which can cause damage to the pump spares.