How can I explain these simple mistakes to young learners?
I no speak English.
(instead of don’t)
You be my teacher?
How long are you knowing my friend?
I have twenty years.
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1) I no speak English.( instead of don't)
In English the negation is formed with not, not with no. Also, in a negation or a question, you usually have to use the auxiliary verb do:
I speak English.
I do not speak English.
Do you speak English?
2) You be my teacher?
The verb be has to be conjugated just like other verbs. They will have to learn that:
I am, you are, he is, we are, you are, they are.
Also, in a question, you usually change the order of subject and verb.
I am John.
Are you John?
3) How long are you knowing my friend?
This one is on a different level, and it depends on the context what would be correct. This would be an option:
How long have you known him?
Here I would suggest you first try to explain the usage rules for verb tenses as they are in your teaching materials.
4) I have twenty years.
That is simply idiom: in English you use the verb be, not have for age. This is simply different per language, and there is no rhyme or reason to it :)