The teacher says it's Yang style. He has never done push hands with me. The form is quite short, 40 or so movementas, I think. He says the long form is just exercise and has no real martial value. He also teaches Liu he ba fa which I have been learning for several months now. The form seems endless. Much longer than the Tai Chi he taught me. So I think he may be adding movements to extend the my time and thus collect more money. He always talks about his lineage in China, but who knows if he's telling the truth. Is it true that Tai Chi was originally a very short form taught by the Daoist?
Possibly, it depends on whose story you want to believe.
I tend to believe the roots of Tai Chi come from a shorter form taught by Taoists and Tai Chi has its roots in Taoism. But I also tend to believe that the thing we now call Tai Chi originated with the Chen Family. That is not to say that there was not something around that was very similar prior to Chen. But the Tai Chi all do today comes directly from the Chen Family.
What is your Sifu lineage from China?
Most Sifu's of Tai Chi have lineage to China, that does not mean they know Tai Chi
Yang Chengfu taught Tung Ying Chieh who taught Sifu Chu who taught me.
Or a sifu near me can say Yang Chengfu taught Cheng Manching who taught William CC Chen who taught him.
I do not know of a Sifu these days that will not be able to tell you his lineage. Lineage does not mean a good teacher but your sifu should have no problem telling you his lineage.
I can also say I learned from my first CMA sifu that was from China, but he learned in a Chinese Wushu University. My Second CMA sifu learned form Tung Ying Chieh, which one do you think really know Tai Chi?
Saying it is linked to China means little.
Also ask him the origins of Yang style. If he claims direct connection to Taoist then he is wrong. Even if Tai Chi originated in total with Taoists it still came from the Chen family to Yang.
I cannot answer you questions about Liu He Ba Fa but there have been a few posts on MT about it and there is or was at least one practitioner on MT at one time.