"Not like that" can be grammatically correct, depending on the context.
No, "I like him best" is grammatically correct. It is a simple sentence in which "I" is the subject, "like" is the verb, and "him best" is the object.
The phrase "Is you don't miss me do you" is not grammatically correct. It should be rephrased to something like "Don't you miss me?" to be correct.
It can be, like in the following sentence. There were many firsts in this historic week.
Yes! That is grammatically correct!
Yes, 'for free', is grammatically correct.
I like the kind of person you are.
This is not grammatically correct. The correct form is 'you do not know', or the abbreviated 'you don't know'.
"That was wrong" is a grammatically correct sentence.
'What a drunkard you are' is a grammatically correct English sentence.
Yes, Almighty God is grammatically correct.
Yes, it is grammatically correct.
Sure. It would also be grammatically correct to write He spoggled his nubbix on the goober. Grammatically correct and meaningful are not the same.