The formal/informal use of pronouns in Czech doesn't date very far back. Old Czech didn't have it. English, on the other hand, used to have it and you was originally the formal expression because you - plural was used long before you - singular. Its nominative form was ye, as opposed to thou (informal you - nominative). The form "you" was used as an object in a sentence.
https://english.stackexchange.com/questions/9780/did-english-ever-have-a-formal-version-of-you
I‘m not familiar with the differences in thou, thee and ye, since they are archaic. Your discussion of the school discussions, exchanges between young students and teachers was interesting.
While I‘m not entirely sure if this always applies in German schools, it probably does. With very young children they probably address the teacher as Herr/Frau xyz + formal you (Sie). Teacher replies with child‘s first name and informal you (du).
I know growing up in the States, it was, for young children, unheard of to address a teacher by first name (I don‘t think we were ever even told what the teacher‘s first name was, but we found it out eventually), and we were always addressed by first name. As a young kid, we used to laugh amongst ourselves about how funny it would be to walk into the class one day and call the teacher by first name- how rude!
But, in the 1960s, we didn‘t have to worry about the Mrs./Ms. distinction, because that was before the Ms. label came around, which didn‘t occur until the women‘s movement of the 70s hit. So all women, married or not, were just Mrs.