The teacher probably thought the omega broke up with his wife and was left with the child, thus thinking the topic was sensitive so never tried to talk about it to respect the omega's space
As for the heat: as seen in the omega's past, whether he was in heat or not, sex was the same all the time, so the teacher most likely didn't notice any changes when the omega was in heat or not...
He was taking a suppressants for heat earlier in chap 1 so probably he hasn't had heat ever since taking them...Why he didn't tell him his an omega tho...
Well in this universe anyone can get pregnant. All men and women that are Alpha, Beta, and Omega can get pregnant, not just omegas.It explains it in the beginning. So I believe that the sensei thought that the omega was a Beta. Also, because sensei never saw or smelled the omega go into heat or talk about it, he assumed that he wasn't an omega.
And he had some problems in the past for being an omega and as you all can that people do not think well of omegas so he hid the fact that he was one
How did the kindergarten sensei not know he was an omega? Either he was able to mask his heat well or they just never spoke about how the child was born. If that's so, they must know nothing about each other.