"Not like that" can be grammatically correct, depending on the context.
'She does not have her book' is grammatically correct.
He, you and I is not grammatically correct. The proper way to say this is you, him and I.
Yes, soonest is correct grammatically.
Yes! That is grammatically correct!
Yes, 'for free', is grammatically correct.
Yes it is a grammatically correct
Currently we have is grammatically correct.
This is not grammatically correct. The correct form is 'you do not know', or the abbreviated 'you don't know'.
I like the kind of person you are.
Yes, it is grammatically correct.
'Rhoda's crazy' is grammatically correct.
"That was wrong" is a grammatically correct sentence.