No, no damage. You should be able to put the shift lever into any gear, without the car running But, an automatic transmission will NOT allow the car to be started unless it is in PARK or sometime in NUETRAL.

Stick shifts sometimes require that the clutch be pushed in, so that when the car starts, it won't move if it is started in a gear and not in NUETRAL

No, you haven't damaged it. In fact, if everything is working right, you should not be able to start the car if its in gear.

is your vehicle a stick shift? If it is it does not damage the car.

Of course not.

No they are made so you can do that . It does not hurt them .

No!

I hit the gear shift and moved it into reverse. The key was in the ignition, I just hadn't turned it to start it. I'm very worried and want to know if I have just damaged my car.