There are few things more annoying, or more potentially harzadous than a dog that bolts out of the door ahead of you. Fortunatley, this is one of the easiest problems to fix. As your puppy starts to rush out the door or gate, quickly shut it in his face. Don't slam the door, just close it quickly enough to bump his nose. After a few times having the door or gate shut in it's face, the puppy will learn that every open door is not to be rushed through.
Alpha defines the space.
For a puppy, this is easily taught by shuffling your feet as you approach. Do not go around the puppy. As for being on the furniture, we let our dogs sit on the couch and chair, but when an Alpha wants to sit down, the dog takes to the floor. If one of my children wants to sit on the couch and watch cartoons with the dog beside her, that is fine, but the dog is still required to get off the furniture first. The dog is called back up onto the couch by Alpha, in this example, one of my Daughters, but it is not allowed to return unless it is commanded to do so.