Amy,

About problem #1, is the biting done with the small front teeth only? If so, it could be a sign of affection or happiness at what is happening to Simba at that time. (We have a Lab that does this). Also Greyhounds have been known to "nit" which is a similar thing.
About problem #2, yes it is not abnormal, although it is disgusting for us, that a dog will eat its own vomit. Canines in the wild will hunt for food and then come back to the den and regurgitate (vomit) the food for their pups to eat.
Problem #3, unless you put the couch against a solid surface, I can't help you with that one! Simba just has to learn not to fall off the couch!