No, it is not. Your following sentence demonstrates it; "You were focusing" is correct grammar for the past tense, and "You are focusing" is correct grammar for the present tense. "You're" is a contraction of "You are".
No, it doesn't.
"Your focusing having been interrupted, you demonstrated some irritation" would be correct, because it makes "Your focusing" part of a dependent clause. The sentence in question, "Your focusing on whom it was that had him killed," does not have "Your focusing" as part of a dependent clause.
"Your" is always possessive. "You're" is never possessive.
It's time to concede and accept the correction.