No touching

And if I'm a man and the teacher is a man and it makes me think, is that a problem?

Is this forbidden?

yes

What prohibition is there in contemplating when she is not ashamed of it?

Why is it not pubic? 2. Reflections are forbidden even without it being pubic. See a review here: https://ph.yhb.org.il/14-04-06/

1- To the best of my understanding, she is not forbidden to him in the law. According to the Maimonides, there is no prohibition from the law in this (one should be protected from all evil) but rather the virtue of the Hasidim. This is evident from his words in the commentary on the Mishnah, and there is a correspondence to this in his language in chapter 21 of Issuu. (But if she is the wife of a man. But there is an additional question here about the prohibition of the wife of a man and the limits of marriage in Acre).
2- Even the prohibition from the rabbis, to the best of my understanding, is only when one withdraws oneself in contemplation, but not in contemplation of the auto. And so is the opinion of the Ezer Mekodesh.

There are many errors in the Halacha you mentioned. The most prominent is what led to the prohibition that you will not change according to the Gam in blessings, which is nothing but words of legend. To the best of my knowledge, the Rambam (and the teachings following him) do not say anything about contemplating fornication. And the Rabba and other Rishonim also say that it is said about contemplating fornication, specifically in the private parts.