When preceded by possesive like "my-yours-his" žena always means a wife. Muž would always mean a husband as well. You never can say "it is my woman" in english meaning it is your wife. Well, you can, if you live in a ghetto. But in such a case it does not really mean the two of you are married. She might be your girlfriend. Not so in Czech.
yes. I know it seems like we made this language complicated on purpose but I promise it is not the case. You can easily have a sentence
Ona má má štěnata. = She has my puppies. Now in real life, one would likely use "MOJE" instead of "MÁ" to claim the ownership of the puppies in this sentence because it would make it less confusing even for Czechs. = Ona má moje štěnata. But there is nothing wrong with "má štěnata"