Can I think "just me" same as "alone"?
Yes. You absolutely can think of "just me" in the same way as "alone" in the context of this clip. Monica is trying to convince Rachel she was eating lunch by herself. The phrase "just me" is also sometimes used as an expression to mean that something is my opinion; my perspective; my thoughts. Ex: I’m not into raw oysters but that’s just me. (My opinion) Ex: It was just me at home. (I was alone at home) Ex: Is it just me or is it really cold in here? (Is it just my opinion) Ex: It's just me. (I am alone)