Nice of you to stop by on this forum. Hopefully we can learn something from each other. So to get started, the first two questions I could think of:
1) What's according to you the function of the dantien? How do you train it?
2) What do you have people do in their first class of Dai Shi Xin Yi Quan?
1) Training the dan tian is of course the primary importance to a Dai Xin Yi Quan practitioner and if focused on throughout ones life. Even in advanced levels, they still spend a lot of time on this exercise.
This reminds me of a story I was told of someone my teacher remembers from the past, in which a man (do not have the name on hand at the mo) who was a cripple (crippled in the sense that I guess he could not walk properly) focused entirely on this exercise and in later years (after practising it for 40 odd years) used to be able to bounce out people from all different types of backgrounds entirely due to his skill with his dan tian. This is confirmed also with my own experience with my teacher as he can perform the same move on me as I do on him and have completely different results.
In my own practice I spend some time standing (from 10 to 20 or so minutes) and then contract and expand slowly from 50 to 100 repetitions. Every 5th repetition I deliver lei/shen (thunder/lightening) which is a special sound which is delivered when you kuai jin (fast power emission).
Dai Xin Yi Quan is rou/gang (hard/soft) with an emphasis on rou jin (soft power) to relax the body/mind and integrate the synergy (whole body power), after some skill is achieved in the soft method, then you learn to fa jin (power delivery). When you deliver you are also supposed to release some power through the voice (not from the voice, but from the internal power). This sound also changes with your practice, starting with a rough sound of "Ha" and then becoming more refined (I do not know how to describe the other sounds to you, sorry).
After doing this for a while I have noticed some interesting phenomena which naturally happens, the dan tian can go off like a gun, meaning when you release it, it is very sudden and the sound has a different quality to it. I noticed this happens when I practice squatting monkey as slow as I can and that further confirms the strict importance of soft power over hard power. It is like you are burnt with a cigarette when this happens.
2. As for what you may learn in a first training session I can only speak from my own line as that is what I have experience in. What you get taught can vary, but for sure you are going to get taught these.
A. Xuan Zhuang aka Di Pan Bu (coiling posture aka lower basin posture
B. Guo Feng Bang (wind wrapping shoulder)
C. Dun Hou Shi (squatting monkey). First taught as a standing posture (zhuan zhuang)
D. Dan Tui Zhuang (single leg posture). Looks like squatting monkey, but on one leg. Very difficult to do properly.
This is already enough, but I know my teacher makes exceptions like for example if foreigners go and visit him due to them not being able to see him again for a while, he will teach a lot more than this, but usually over a week or 10 day period.
Those above moves need to be practised every day for a long time (I cannot say how long) before you learn footwork and the Wu Xing Quan (5 elements). I believe it is best to be taught few moves correctly and master them than try and take on too much and especially try and learn certain moves before building a foundation. If you do not learn the basics properly, you are laying a recipe for disaster.