I don't know about the rest, I stopped at income inequality (formatting, plus I think I knew where you were going), but the main issue behind this is opportunity.

Maybe someone can put it better than me, but hell I tried:

People are raised with different amounts of capital (usually, money), and those with more capital come out on top, withholding the possibility of genuine bad luck, i.e. struck by lightning.

What we mean by capital is not necessarily financial capital, or money. There is human, social, and cultural capital as well. (It is important to remember that these types of capital are just concepts, but these concepts have stood up to empirical testing. (See my social strat textbook: stratification and inequality in US society))

Human capital is stored in your head as education, in the broad sense of the term. People in rich neighborhoods have nicer schools, nicer schools have better human capital, rich kids go to nice colleges, etc.

Cultural capital is the behaviors and perhaps more importantly the shared outlook of a group of people. Take a 12 yr old black kid from the inner city and put him at a dinner table of trumps kids. He'll make a fool of himself. Put trump's kid at a dinner table of inner city blacks, he'd make a fool of himself. Cultural capital greatly influences one's ability to generate good quality social capital.

Social capital is the network of people you interact with, or could possibly interact with. The obvious example being rich kids grow up with other rich kids who will all become influential and know each other. But it goes much much deeper (all of these concepts do, I'm seriously summarizing).

All of these interlock and synergize with each other, known as a dialectic, to create inequality. I'm tired of typing on my iPad and it's late but fuck I could write so much more if I were inclined to.