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There are actually two questions here.
If you're worried about lead from the pencil, they are actually made of graphite these days, so lead poisoning doesn't really happen.
But, the pencil itself could potentially cause a problem. Depending on what they eat, sometimes inducing vomiting is a good idea. But, if the object has the potential of being sharp coming up, this is not recommended. It is better, if the object is going to cause a problem, to have it do so in the intestinal tract.
The pencil could cause some vomiting and diarrhea, or it may pass without any problems. If it does cause symptoms, you'll need to have him seen by a vet. It may be a simple gastroenteritis from irritation, or it may be much more severe. But, you are playing a waiting game right now. You are waiting to see if symptoms present.
What you can do right now is feed him small amounts of white bread. This will help bulk things up. The goal is to surround the bits of pencil, so they don't cause as much irritation going through. But, don't feed too much. This may make him vomit.
Good luck, and please let me know how he does.
There is no right way. If you go out and look at dog training, there are about 50 different approaches--positive reinforcement, pack leaders, alpha training, discipline both physical and verbal. It really depends on your temperament and beliefs. And, the temperament of your dog.
The key thing is that you have to catch them in the act. If you catch them 30 seconds after the fact, they have no idea what you are mad about. I've heard people say that the dog knows they did something wrong--they do, because they can tell you're mad, but they have no idea what it is. You've got to catch them in the act, and pick the appropriate training discipline.
I have four dogs and they are all trained differently. One is dominant, one is fearful, one is stubborn. No one training method works for all of them.