On Belief Propagation and its use

Adding to sbos's answers:

1. Yes, exactly. BP computes the marginal distribution for each node.
2. Not exactly. This would be done by some form of parameter estimation (i.e., maximum likelihood, sampling, regularized maximum likelihood, maximum margin, etc). Most of these will require that you run BP to get the normalizing constant for the gradient (but maximum margin will only require that you run max-product, not sum-product)
3. I'm not sure what you mean by CPD, but to compute the likelihood in the case of latent variables you have to run BP twice: first over the latent variables to compute the expected score of the observed configuration and then over all variables to get the normalization constant. EM is an approximation to this that maximizes a lower-bound on this likelihood which is often easier to compute.

Of course, to be correct you'd have to run actual belief propagation over junction trees, not loopy BP, in the cases above.

At first, BP does inference only in models without cycles (i.e. trees, chains).

1. I'm not sure I understand your all of your questions, but BP get us not only the marginals, but also optimal configuration of hidden variables.
2. What is conditional probability tables? Do you mean all the $p(y|x)$ probabilities?
3. I also misunderstand what's the question about. BP is very similar to Viterbi algorithm, except that Viterbi handles only sequences and BP is for more general cases, so it might be useful for you to examine it first.