That distinction in your previous training is very shallow. Let's try that again in a more abstract way. What can a Yin-Yang Master do that a Yang Master cannot?Well as it was told to me during my training with Pervy, at least as far as the restrictions within the techniques themselves go, a Yang Master is someone who has completed their Yang training, and Specializes in Yang. So my assumption would be that a Yin-Yang Master would be the same, someone who has completed Yin, Yang, Yin-Yang training, and has the full Yin-Yang specialty on their bio.
I remember White Tiger having an effect associated with it that involved impacting the Yin Chakra within the targets body, affecting their ability to utilize Yin and related fields because they essentially had so much Yang Release Chakra injected into them that it disrupted their own balance between the two. As far as I'm aware this is the only way one can directly manipulate Yin Chakra without having the field itself, but it's only a result of overwhelming your opponent with such concentrations of Yang Release Chakra. You aren't directly manipulating Yin Release Chakra but rather indirectly affecting it, which I think is an important distinction to draw. In a roundabout way the answer to your question is yes, but only indirectly, as a result of creating an imbalance via increasing Yang Release Chakra.
As for your second question, personally I don't believe it's possible to make one "better" at Yin because you're reducing your Yang Chakra. Best you'd achieve is making yourself physically weaker, without actually increasing anything Yin related, because negatively impacting one isn't the same as being able to enhance, or directly control the other.