I was let go on good behaviour from my teaching job because I was out too long,
Can my old employer tell my disability to my new employer

Your old employer can tell the new employer anything they want as long as they tell the truth. And if you hide your disability from the new employer you could lose the job once its found out.

Yes, and it is often a major question on some back ground checks. Also was it a workers comp disability or another type. But normally this is records that can be checked when you sign for the new place to do a back ground check on you