Yes. What is not correct is your putting the article "a" before grammar.
no_____If the sentence is You do do that (meaning You are in the habit of doing that) the grammar is perfectly correct and the sentence 'does have correct grammar'.
That sentence is grammatically correct.
No.
The grammar in the question is correct.
"Roger and I appreciate what you did" is correct grammar
The correct grammar is "Between you and me."
The correct grammar for this sentence is: When did your friend come?
Yes, "you were correct" is correct grammar. This sentence is in the past tense and conveys that someone was right about something.
that is correct grammar
Yes, that sentence is correct grammar.
The sentence is grammatically correct.
That sentence is grammatically correct.