I had my early English education in China, we were taught some weird English grammar that I have never seen in the USA. I now think those are fake grammar rules

I had my early English education in China, we were taught some weird English grammar that I have never seen in the USA. I now think those are fake grammar rules. One example is, if you say "no + a noun". the noun has to be in its singular form. I remember they actually tested this rule during exams. I was shocked when I came to the U.S and saw the sign saying "no dogs allowed" on a door.