If your air condition is on can you still have windows open in house with out hurting the air condition?

It will definitely cost more money and put the air conditioner under a higher load for a longer time. So yes it will burn out the air conditioner faster, if it is pumping out air that is significantly different (cooler and humidity) than the air coming through the window. The reality is that if a window is open the air conditioned air will go out the window and that air con air costed you time and money.