Housebreaking is totally different than "dog training the clueless" (the OP's words in her first post).
As I stated in previous posts, keep your dog in a crate when you're not home (good for you that's already in place!). When you're home, keep the dog confined to a small area; probably your kitchen, assuming you don't have carpeting. NO house roaming priviledges until there have been no accidents in the kitchen for at least a month. Housebreaking a small dog is very different than housebreaking a larger dog. Smaller bladders mean they have to go out more often. If you've ever been pregnant, think of how much more often you had to go to the bathroom during that time than you normally would....you had a smaller bladder because of the baby taking up more space. Same idea with smaller dogs; their little bladders fill up quickly. Being taken out in the morning, at night and "anytime it's been in the crate for a period of time" is not enough IMO. To train with a bell on the door, you help him paw it, then say in a happy, excited voice, "Oh, you have to go out! Let's go outside to go potty!" Once outside, you should be very quiet, avoid eye contact with him, and basically detach yourself from him while walking around with him until he squats/lifts his leg. After that, you basically do a cheerleading routine whenever he does anything outside; lots of praise, head and belly rubbing, etc. I don't use treats for anything when I train a dog. As you've stated, the dog gets distracted by the treat, and comes to expect treats in order to follow your commands.
As you got your dog from a pound, you don't know when he was separated from his mother. If it was before he was 12 weeks old, he may not know "how to be a dog".....so learning to use a doggy door could take a lot of time. You need to have him going outside consistently, no accidents in the house for several weeks, before going on to the next step of using the doggy door to go outside.
As for chewing, make certain there is a basket of doggy toys in the kitchen, on the floor, where he can reach them. Try balls, nylabones, plush squeaky toys, etc. Pet stores have a wonderful selection of different things with different textures. Give him a "chewie" (my dogs love pig wraps) every day. Puppies chew; when you catch him chewing something he shouldn't, get down on his level, say in a firm, strong voice, "No! We don't chew wood/the flooring/the rug...." whatever the case may be. Then immediately give him one of his toys and praise him when he takes it and chews. Puppies (and some adult dogs) chew. If it's a solid surface, like a table or chair leg, applying some bitter apple can be a great deterrant.
Having said all of that, I do hope that in addition to training to eliminate negative behaviors, that you're able to find the time to do some obedience training as well. Having a polite, well trained dog who listens to you is so much fun!
