Alternative "My husband must be able to cook". Was this sentence for a husband who exists and will cook today or an unknown future person who will be required to cook?
That's an interesting question. The Polish sentence here sounds more like she's trying to teach her husband how to cook and then says "Don't worry, he'll be able to cook soon, he just needs a few more lessons".
What you've suggested sounds more like as if she was asked what would be her perfect husband and then lists things he'd have to be able to do, but in that case, in Polish, you'd say something like: "Mój mąż powininen umieć gotować" or alternatively "Mój (idealny) mąż musi umieć gotować".
Your sentence is correct technically, but... pretty weird, it's like you asked us to define the difference, or something... "Jaka jest różnica", with an adjectival 'what' (What is the difference) is the natural way to say it. But it's great that you try writing in Polish :)
Well, 'móc' would be translated as "to can" if only this was correct in English. So "mogę" is "I can", "I am able to", "I am allowed to" and similar.
"umieć" refers to having some skills, and being able to do something because of those skills. "Mój syn ma siedem lat i już umie czytać" = My son is seven and he already knows how to read/can read". "Nie umiem jeździć na rowerze" = "I cannot/I don't know how to ride a bicycle".
Well... most Polish people probably wouldn't bat an eye, but according to the language rules, we should avoid using a double infinitive. So in this case, it should rather be "umiał gotować".