Translation:I want the hamburger which costs five euros.
Clearly here που is a "that" (narrowing relative pronoun); it implies that, of the hamburgers available, I want a smaller subset (one, in this case).
Is there a distinction in Greek between "that" (narrowing relative pronoun) and "which" (expanding relative pronoun)?
E.g., in English, there is a great difference between the two following sentences:
• "My wife, who is making tacos tonight, is a great cook."
• "My wife that is making tacos tonight, is a great cook."
Does modern Greek make this distinction with που and (an)other word(s)?
Yes, if you are asking someone to bring you something you would use "*I would like..."
Yes, "interlocutor" is right if a bit formal. It's what we use when we do "Oral examinations". I guess in colloquial Eng. we'd have to say: "the person you're speaking to" or "the person you're addressing."