All forms of Tai Chi that I know of have very similar looking versions of Single Whip except for the Wu-style. In Wu-style, it is done in the horse stance (with some small variation to the weight distribution). Why is this? Is it meant to make the target smaller? Or is it meant to make the waist movement more intense? What's the purpose here? EDIT: My teacher said he's not qualified to talk about other styles of Tai Chi, so I figured someone here must practice at least two styles and could tell me the purpose of this difference.
As to 'why' Wu style has a horse-stance position, I can't really answer.. Though the Yang style I practice has single-whip in a side-horse stance. The way that I see it, a forward stance may generate a longer Jin, whereas as side-on position would lend itself to a shorter, sharper Jin. Not saying the two are mutually exclusive, however.
It depends on - the distance between you and your opponent. - what your finish move may be. If you compare the following 2 moves, the - 1st one is more like horse stance with "backward and upward" motion. - 2nd one is more like bow-arrow stance with "forward and downward" motion.
I think it's only done in a horse riding stance in the slow form. In the fast form it's done in an archery stance, which I believe is how other styles do it. The 'orange book' says that the horse riding stance is done to strengthen the legs. I can't think of anywhere else that we do that stance apart from in single whip, so that might be the explaination there. I think it's probably misleading to over-analyse the slow form in terms of martial application. The slow form was developed mainly for learning the fundamentals and for strengthening and conditioning the body. For martial application you really need to study the fast form.