What should we think about – and what should we teach our children about – non-Jews and the non-Jewish world?

Do all non-Jews hate us?
Does exposure to the non-Jewish world help or hurt our children when they grow up?
What are the hazards of teaching children negative attitudes about non-Jews?
What separations did Chazal institute between us and non-Jews? Why did Chazal feel that was necessary?
Do we need to be concerned with causing “Aivah” (animosity) with non-Jews, even if we are doing nothing wrong?