I colored my hair and it came out a light auburn and I don't like it. Can I recolor with a dark brown. Will that cover the red?

Yes. It should cover the color. You may or may not have a slight tinge, but if the brown is dark enough, it should be okay. Just remember to condition your hair well afterward to avoid damage :)

Yes. Since the pigment of the new dark brown color would be darker, it would cancel out the red and of course darken your hair.