You can wear whatever you like as long as you are comfortable. Almost any color can go with another depending on all the components involved. If you love your brown shoes and black socks, then tell your wife or if you are neutral ask for her suggestion!
You should listen to your wife on this one. Wearing black socks with brown shoes is a bit taboo. In fact, in most cases mixing brown with black at all is taboo. Stick with something neutral like beige or tan or even another brown, but no matter what you do, avoid the black!
No, you should never wear black socks with brown shoes or visa versa. It is best to match them. If you are wearing boots, or something where it is impossible for them to be seen, it's ok.