A Few Puzzles for a Rainy Sunday

Five old puzzles to brush up on your logic skills before the GREs:

(1)
Yesterday I ran into my colleagues Eric Wiland and John Brunero, who were trying to sneak out to watch the baseball game. I asked Eric:
"Is any of you a truth-teller?"
Eric said something that sufficed for me to know the answer to my question. Are Eric and John liars or truth-tellers?

(2)
You just met Brit and her daughter Becky at the APA smoker. Becky says:
"Either I am a liar, or my mom is a truth-teller."
Is Brit a liar or a truth-teller?

(3)
You're walking down the hall in Lucas Hall and bump into my chair Gualtiero Piccinini. You ask him:
"Are you a truth-teller?"
As he is answering, there is so much noise in Nora's office that you cannot hear the answer. So you ask again:
"I couldn't hear what you said, did you say you were a truth-teller?"
Gualtiero replies: "No, I didn't say that, I said I was a liar."
Is Gualtiero a liar or a truth-teller?

(4)

You are on your way to the APA smoker when you come to two doors. One is the door to the smoker. The other is the door to the best bar in Atlanta. There are two APA people in front of the two doors, one who always lies and one who always tells the truth. You don't know who is the liar and who is the truth-teller. You are allowed to ask one single question to one of them to figure out which door to open. What question should you ask?

(5)

You got a fly-out. As you are talking to the Dean, you realize that he has three boxes on his desk. There is a sign next to the boxes that states that one box contains two white balls, another two black balls and the third a white ball and a black ball. You don't know which one contains what. Each box has a label saying which balls it contains. One label says "TWO WHITE", another says "TWO BLACK", and the third says "ONE WHITE, ONE BLACK". But none of the labels correctly reflects what is inside the three boxes. To ensure that you are hirable the Dean asks you to change the labels and put them on the right boxes. But, he says, "You are only allowed to open one of the three boxes, take one ball out of it and look at its color." Which box should you open?

Feel free to put your answers (and how you got to them) in the comment section.