That might actually be caused among other things by a higher representation of African-Americans in the US military. Turns out, being a US soldier can have all sorts of health consequences...
I'd bet there is a stronger correlation between homelessness and incarceration rates. Incarceration in this country is very racially biased and it can be very difficult for ex-cons to find decent jobs that keep them off the streets. A lot of them end up with the choice to either be homeless or reoffend.
I doubt it. I'd say having cities and large neighbourhoods that are effectively no-go zones for well-adjusted families has more to do with it. These are literal and figurative breeding grounds for anti-social behaviour.