Point #1 is being debunked more and more by the year:

https://www.rawstory.com/2012/02/science-overturns-view-of-humans-as-naturally-nasty/

Even Darwin saw cooperation and empathy in animals. Empathy is required for cooperation and cooperation is the foundation of the success of the human race. Check the movie, I am - The Movie and you'll see some great evidence of cooperation as a basis for life.

Humans are competitive if they are trained to be competitive. In materialist, Protestant Work Ethic, Western civilization, we are trained from cradle to grave, to be competitive.