I played a real organ - in a cathedral!
It was very powerful and felt like I was inside the music.
Re technique - The organ teacher who was sitting with me said I should aim for quite the opposite of legato. If you don't detach the notes, they all bleed into each other and the music sounds awful.
"the note doesn't die away as long as you have your finger pressed on the key, and also the note finishes immediately when you release the key."
Yes, and this is why it is a very precise instrument while the piano (where all notes continue for a while) really isn't. And on top of that pianists use the pedal which extends all notes you play even further. This doesn't matter when you are playing a single melody but it kills the contrapuntal polyphony of the Baroque period. It's why Bach in particular sounds so incredible on the organ and the harpsichord but not on the piano.
(Notes die as soon as you lift you finger from the key in the harpsichord, as well. Another similarity between the two instruments is that the volume of a note does not change depending on how hard you hit the key - another reason why Baroque music doesn't sound great on the piano).