Technically, 'I have no pen' is correct. Instead of using 'I have no pen' or 'I do not have pen', just use 'I do not have a pen' because it is the best way to phrase what you want to say.
No, the question is not grammatically correct. It should be "Does she have a pen?" using the correct form of the verb "have" for the subject "she."
They are all correct, although the first two, being without contractions, are preferred in writing.
The sentence "There are five pens in the box" is grammatically correct.
None of these are grammatically correct. They should be, "He has to come here." "I have a pen."*and "I have to go there." * Unless, that is, you meant, "I got a pen (out of my purse/out of my desk/out of my backpack/etc.)"
Ruins is plural so the grammatically correct form is The Ruins of Windsor are
Yes, it is grammatically correct to end a sentence with the word "so." However, it may be informal or conversational in style.
"Not like that" can be grammatically correct, depending on the context.
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.
Yes! That is grammatically correct!
Yes, 'for free', is grammatically correct.
The phrase "You are not knowing" is not grammatically correct. Instead, you can use "You do not know" or "You are not aware."
"That was wrong" is a grammatically correct sentence.