It is not essential to have air pump in a turtle tank. Turtles are more filthy pets as compared to fish so changing water is more necessary than it would be for the fish. Point is, keep turtles clean with regular water and filter cleaning and then you have nothing to worry about.

 As long as you don't have fish in it then no... Turtles get their oxygen directly from the surface air.

 Turtles are fun pets, but if you have small children around, you shouldn't let them hold them for too long, as they are known carriers of salmonella, so if you do let them hold them, make sure they wash their hands thoroughly after handling them.
Now on to the air pump, they don't need them, they are air breathers, just keep from putting too much water in the tank with them, just deep enough so that they can swim, and place a clean rock in the tank so that they can climb onto it to warm from the warming lamp that you should have externally attached to the tank.
Depending on the size of the turtle, you can fill the water from 4 inches, to about 6 inches. Make sure that you feed them on a schedule, so that they become familiar with a routine, and do the same with the water.
You should change the water about once per week. Hope this helps.