Michael answered your question well. I'll just answer the 2nd part of your question.
If you're expressing "You have the most beautiful eyes", I would say:
If you're expression "Your eyes are the most beautiful", I would still say:
"你的眼睛是最美丽的" is grammatically correct. But... it's like saying I want you to know that your eyes are the most beautiful features on you.
我的房间是红色的。(My room is red.)
Here, I'm emphasizing the fact that my room is of the color red.
我的房间红色的. (My room is red.)
Here, I'm just saying that my room is red.
In this example, there isn't that much of a difference, really. In day-to-day conversations, you can get away using either one. But let's not forget also, that what we say also depends what we were asked and what we were trying to express/relay to the other person..