From your description, my first thought definitely would not be mange. The problem with assessing/treating a condition like this without the benefit of a vet is that unlike (most) humans, animals lick/chew/scratch insults to their skin/coat. The yellowish crusts sound bacterial - in a human, we would start with something on the order of impetigo and work on from there depending on the health of the person. Having said that, an allergic reaction could trigger something that might end up looking like your description as well. Dogs do pick up dermatic viruses (hygiene and other pet contact caution). Staph has already been mentioned and is always a possibility once there is breakdown of skin for any reason. The hair loss is a little concerning. If your dog is not agitating the coat due to itch/discomfort, the hair loss as a result of the condition would have to be brewing for a little while. I would not panic but I would want a vet to see this asap. I agree also with doing an internet search and soaking up everything with an eye toward questions for the vet. I personally would not risk trying to treat this without the input of a vet. Best of luck to you both! Please let us know how things turn out.