1) The answer to your question would be that the correct use of the missing word in the sentence above is the following one: Your. That is, your answer would be D. "Your" is a possessive determiner, that is, it modifies a noun by attributing possession or the sense of belonging to someone or something.
2) The answer to your question would be that the use of the missing word in the sentence above is the following one: I walked right past him in the mall and didn't realize it. That is, your answer would be A. A verb indicating motion is already in the sentence (walk), so you shold add "past" which will function as an adverb.