There aren't enough good schools/teachers out there who are qualified to teach the true martial side of Taiji. But from mym experience, Taiji is a base to build on, or to add to a base for martial arts. Because of it, fighting, or even using specific applications becomes almost meaningless because you can knock, or throw people over so easily. All the basic things, although push hands is also something you need (weird he doesn't teach it), that you are doing, are all your going to need in the future.
Do your rsearch if you want to learn more apps etc.
Truth comes from the absolute stillness of the mind...