Why is "la cucina e lei" not correct?

The kitchen is her?

I cannot be "e la sua cucina"?

Is "La cucina è della." wrong?

what is difference between sue and sua

"La cucina è la sua" is the correct answer it says, but is "La cucina è sua" correct too? Because I just answered one (incorrectly, apparently): It told me that "The knife is ours" = "il coltello è nostro" and not "il coltello è il nostro". Are there special rules when it comes to plurals? Or is this an error? (you can see it here) https://www.duolingo.com/comment/402781

I cannot use accents on my mobile

Can somebody explain what is the difference between "la cucina è la sua" and "la cucina è sua"? Both answers are accepted by Duolingo, but do they mean exactly the same?