Hi Robert,
Thanks for you response.
I just think that the thirteen postures are so neat, since if you get even a basic understanding of how they work, you an do some really profoundly cool things with them

I agree wholeheartedly. I always wonder why more people don't do push hands, given how much fun it is. I have pushed with people almost twice my age and half my size, and twice my size and half my age, and have had a blast with both genders.
I'll try to answer your two questions, but please know that I'm trying to empty my cup a bit recently, so the answers may seem a bit convoluted in an attempt to try not to assume that I actually know something about this topic
As long as there is a modicum of politeness, I prefer straightforward statements. Tai Chi is already so hard to understand that too much hedging and hawing can be counter productive. I can learn better from clear and wrong than from vague, but correct.
In terms of changing from yin to yang, what I meant was that people generally get stuck on one energy and don't change freely enough.
I know I used to always get stuck trying to make pushes/pulls work and only changing directions very choppily and jerkily.
I try to teach the Association's system. We start with eight standard applications, one for each energy, that you are supposed to learn to do smoothly. They involve combining anywhere from one to six uses of energy in order to feature a particular energy. We start the applications from the vertical circle that cycles through the four square energies. Then we learn variations. Starting from the vertical circles forces you to learn how to chain the energies and set up the conditions that create the opportunity for success. I would say that each application always has a Yin and a Yang side.
As for changing between gates: same kind of thing I think. It is easy to change gates in cooperative exercises, but not so much so in freestyle.
I tend to teach in a semi-cooperative way. Once the person learns the mechanics of an application and gets to work with it a bit, I move only if the person makes me move, so that he or she can get a feel for what his or her use of energy actually does. I find that if someone does the applications smoothly, you cannot easily prevent them from "knocking on the door" of the gate" or even sometime from stepping in. After learning and mastering counters, however, you can usually stop them from stepping all they way through the gate.
If the original technique is executed in only a mechanical way, you usually do not need to counter much at all. We also often teach counters to counters, so that you can begin to learn how to move smoothly through multiple exchanges of technique without interrupting the flow of energy. Some counters lend themselves easily to this kind of continuous flow, but some do not. Some involve uses of the eight energies, but many involve other uses of energy I do not really have names for. The counters are also dependent on the relative level of the people involved and will not work on someone whose Tai Chi level is sufficiently higher than you. The more you learn about energy, the more options you have and the more subtle your technique can be. This search is what I find to be the most fun.
I like the rough side of martial arts.
I like this as well, as long as folks play with a gentle heart and respect for differing abilities, goals, and personalities. I like being bounced around and throwing others around; however, most of our techniques can be done in dangerous ways. Of the eight semi-standard techniques we learn first, there is only one that I do without a major concern for safety and that is Press. All the other applications need to be modified for safety in some way (speed, positioning, or power) to ensure that no one is injured and everyone can practice for a long time. Once these rules of caution are respected, you can still bounce each other off both feet and even take each other to the floor on occasion. Or, if you don't like the rough aspect of things, you can still keep things quite gentle and learn a lot that can be helpful for people who do Tai Chi only for health.