The word cocina in English is cooks so that makes it a verb
Hey!
While both are often used, the most accurate answer is probably answer a:
The "personal a" is necessary.
Why?
Well, when we say: "Quiero a mi esposo Jorge" we are talking specifically about the husband, that is: "lo quiero a él". Therefore, the "a" is usually used on these occasions.
What's the question? I am Mexican American and I don't understand what you're trying to ask.