Bayes factors can be used to compare models that aren't nested and, therefore, can't be compared using other approaches (like a likelihood ratio test, for example). All of what you said above is can be distilled down to a few main points:

1. PhyloBayes will use thermodynamic integration to calculate the marginal likelihoods. Other approaches that estimate the marginal likelihoods, such as taking the harmonic mean, have been shown to produce inaccurate results.

2. You ought to have estimates of the marginals from your data. In your example, they are testing two models. It is possible to compare other models, too. Once you have your Bayes factors, you have evidence for which model is the best fit to your data.

3. What you want are the likelihoods for your trees given the model. The trees themselves don't provide any information that could be used to select among models absent the data and some info about the model itself.

Hope this clears some things up.