You can't really think this way. You can't imagine how many people speak a non-grammatical English, even if they are native English people.
She's a teacher and probably spent years studying the correct English (grammar, spelling, etymology) and not the one that everybody speaks.
For example, you can hear a lot of people say "it don't matter" or "what you said?" which are okay but only as an everyday English, and some people won't even notice the mistake. But both are grammatically incorrect.

I think this problem is the same everywhere whatever the language.
You're right that I can't imagine how many people speak non-grammatical English even if they are native English speakers. This is because I have never met such people. Hope I won't ever meet them.

What you said? Is cleary wrong, and sound wrong to most educated people. However, "I'm going to school tmorrow" sounds fine to almost everybody. I think you will find that in modern revised English grammars this phrase is fine. It is only in old books that this will be described as wrong.

I suppose the same can be said for the Russian phrase "Завтра я иду в кино".
Sounds good to me.
You have always got to keep up with "modern revised English grammars". I don't think English changes so quickly you constantly have to worry about whether something new was accepted
the other day. I mean that grammars change fairly quickly if we see them as part of language.