Esposo (spouse) is a bit old-fashioned, I rarely see people using it. Marido (husband) is the standard one. Homem (man) is a lot more informal and it sounds a bit possessive, so I only see it being commonly used when picking up a fight, e.g.: "Não acredito que essa vadia deu em cima do meu homem!" "I can't believe that ❤❤❤❤❤ hit on my man!".
For women, both esposa (spouse) and mulher (wife/woman) are commonly used.
Esposo is more formal than marido. Homem isnt the same. If one says "ele é meu homem" it sounds too rude. But you can use esposa and mulher interchangeably to mean wife
So, it is not rude to call your wife "your woman", but it is rude to call your husband "your man". Oh, Portuguese! and likewise, I think, in Spanish! If something is commonly used, does it really mean it is not rude?
I totally understand what you feel. Actually I found myself kind of frustrated when learning Portuguese. Just say something more, Duolingo always preset the correct answers in masculine form, that's pretty annoying.
Would it be meu esposo and hence a minha esposa? Or would it be meu esposa as well
Can you also say "ele é o meu esposo"? Like with the article "o" (and same for "a mini esposa" etc.) ?