perfect.

It's more natural to say; I am not happy with this situation or I am very unhappy with this situation

Yes, this sentence is okay. More often you will hear, "I am not very happy with this situation."

I agree with Rob that you'll hear "I'm not very happy with this situation" or "I'm not really happy with this situation" (my preference). "I'm not quite happy with this situation" sounds pretentious to me. My response would be, "What do you mean by 'quite'? So, are you happy or not?"