Is natural selection a universal process?

The probability of life evolving into a complex form is one of the factors in the Drake equation. Drake himself estimated that probability as 1.0, for what that's worth.

He had that confidence precisely because descent-with-variation seems pretty certain to be a universe process because it's so straightforward. If you have something that reproduces imperfectly, eventually more complex versions will be the result. Even the "natural selection" part is optional if you were just imagining searching through the vast space of genetic possibilities, but finite resources make selection inevitable.

Generally speaking, yes.

Since a female is both xx chromosome and the male passes down the x chromosome, than the offspring would be female since a female is xx.