Of course it has happened. Okay, one can assume it has not happened given no evidence that it has, but this is a big assumption, even given CI indexes of ca. I agree fully. An entire tree is not really a single hypothesis.
Bremer support is fine.
Not as such. This seems to be a critical area we should all know more about. If they don't pass the test, then more character data are needed. The criterion is that there is a reference set of intermediate taxa between the man chimp and the dog. Thus it makes parsimonious sense that macroevolution or lots of convergence were very improbable in this case, since gradual evolution is modeled.