In the Name of God, the Compassionate, the Merciful.
Hi!
Greeting conversation:
Sara: Barney, what’s up?
Barney: Hi Sara. Nothing much. I’m just hanging out. What’s up with you?
Sara: It’s a good day. I’m feeling fine.
Barney: Well, I have to go. Nice seeing you!
Sara: Later!
1- What does “What’s up with you” exactly mean here?
2- What does “I’m just hanging out” mean here?
Thank you
It means:
“What are you doing?”
or
“What is happening?”
It’s almost more of a greeting than a serious question. Although some kind of response is usually expected.
“Not much” is a common response. Unless something important is happening. In which case a more serious answer will be given.
It’s much like the greeting “How are you?”. It’s a greeting as much or more than a serious question.
“Hanging out” means they are just passing time not doing much important or exciting.
“What’s up?” is somewhat old and not said as much by younger people today. It was very popular in the 1970s.
“Sup?” is a more modern abbreviated version of it.
or
“Wusup?”
This reminds me of the old television ad. Hopefully you can understand it. This is exaggerated, but not by much. People used to take this to extremes.
Again
Thank you so much, NearlyNapping 
Very nice.