About projector (beamers) usage
To the first question yes, you can, but try not to do it- the filament of the lamp is very delicate. 
Respect to your second question, that's true! Turning your projector on and off decreases the life of the lamp, and that's true with most lamps. It also probably reduces the life of the components inside the projector, but that's not something we can go into detail here.

Good luck!