Good advice from echooos and Danae, I would only add, never lie to your mate and record everything if needed.
Tell the person immediately NO and next time with your partner present.
A friend's partner shows interest in you. Would you tell your friend?
I would try and handle this myself, being absolutely clear with the partner about my non-interest and his possible betrayal. I would also tell the partner that unless they want their behavior broadcasted, they would cease and desist with the unwarranted attention. They also should considering breaking up if all they want to do is fool around with other people.
That depends entirely on what type of "partner" you're talking about.
Unless it's a spouse or fiance ... There is nothing preventing them from having multiple "partners". In which case, I'm as free to be with them as my friend. Of course, I would tell my friend - but I wouldn't care if they said "no".