My dog is very nice and has never shown aggression away from home. He loves to go to work with me, ride in the car and go anywhere. He is very mild mannered and has never shown any signs of aggression away from home. When we get home, it is completely different. I can't even pet him without him flaring his lip and showing his teeth. We have gates that keep him confined to the family room and kitchen (which is a very large space), and when I step over the gate he usually barks and runs at me growling and barking. Many other things can make him angry at home, such as looking at him too long, picking up something from the floor, asking him if he would like to go outside, and sometimes even feeding him or putting water in his bowl. He is a combination of many breeds, including Rat Terrier, Jack Russell, Chihuahua and Corgi.
You've got a mix of a number of high energy, frequently aggressive breeds. It sounds like the dog is defending territory it has claimed as its own, but the other issues you mention suggest that you seriously need a very good trainer. Positive reinforcement is key.
All of the behaviors you have described are more or less common, but they are also absolutely unacceptable. A decent trainer should be able to help. I recommend that you find one as quickly as possible.