You are really asking for too much in one question, so your answer will be broad.
FRIENDSHIP: Relationships in this work demonstrate that most people do not have significant friendships. Evidence can be found in Gatsby's funeral (Chapter 9) and Jordan Baker's coming and going so quickly out of the lives of people she would call friends. Everything is surface level.
HYPOCRISY: This occurs as we see Daisy enter into a cheating relationship after she looks down on Tom for being in one. (Chapter 6)
CARELESSNESS: This is demonstrated in every party as the details of the periphery are shared. Women spill on their great evening gowns, and a terrible accident occured in the driveway. Alcohol is consumed in dangerous amounts. Myrtle's death occurs without a care from Gatsby of her condition. (chapter 7 end)
THE AMERICAN DREAM: We seek success, liberty, and the pursuit of happiness. None of this is attainable unless we have life. Because of the deaths of Myrtle and Gatsby, neither of them will ever experience success or liberty. The American Dream requires work, not just physical and occupational work, but relational work. See the link below for further information.