I always thought is sounds better on...My teacher came by today and she finally heard the Galaxy II Böse with Concert Room reberb [toned down] through the headphones. She said it sounded nice, but not real, processed. I removed the space setting and she said it's much more closer to what the player standing at the piano hears and recommended I practice with the reverb off and only use it when I record myself.

So the question is, should it always be off? On a DP, is it put just to give a false impression of the strings resonating thorough the piano body and then back to the environment? Does it have any influence on practice [ie. are you able to hear "things" better/clearer?]

That's pretty much depending of your own preferences. I would say, without reverb it sound more direct, and it's quite fine if your DP supports additional effects like damper effect and sympathetic resonances (it's somehow similar to a reverb).

The reverb can give you a somewhat impression of a more open / concert hall sound, but of course it's not the real thing and only fake (like the whole DP anyway BTW).

If you are practicing with speakers, the room you are in with give you a little natural reverb. However, if you're using headphones,there's nothing natural for the sound to bounce off unless there's space between your ears. With headphones, a touch of reverb will make it sound like you're playing on a real piano in a room.

When I record myself I turn reverb off. Audacity, the program which captures the sound directly from the dp, lets me adjust the reverb to my liking. Otherwise it's always on.