Video 1, I don’t even like the way he is doing grasp the sparrows tail
Video 2, I agree with 1 & 2. 3 and 4 are BJJ or other style, not Taijiquan. Nothing wrong with them, good to know, but if it were me, at 3 I’d have gone for Kai (Shoulder). 4, if he steps again, I may just stomp on his foot and then Ji (press) or An (push).
The problem with looking at taijiquan applications, and this will not make me friends in the taiji world, but the problem is the arrogance that comes with it. I once worked with a guy who was, to be kind, pathetic in applications. I tried to correct him, I was actually teaching per request of my shifu (my 1st shifu) the guy stopped, looked at me, and said rather loudly... "I don't DO martial arts.... I do TAIJI!!!!!" and he turned and walked out the door.
It is not magic, it is training. I will say the application of taijiquan is a bit different than other styles, taijiquan tends to not force applications, just applies them. I have worked with several people using qinna, and I could always tell you when they were about to apply it, some I could stop, some I could not (couldn't stop Yang Jwing Ming). However my Yang Taijiquan Shifu, I could never tell, I was just locked.... asked him how he did that, his answer "You lock yourself". Meaning he is very aware of my position and when I am in the right one, he just applies a little pressure and I am locked.