1. is
This is because it's a single chunk of time.
2. is
This is because it's one dish.
3. quite
I don't think that both are possible. In this context, "rather" would suggest a negative quality.
For example. "Would it be possible to have another room? This one is rather small/rather dark/rather noisy".
"...but it's rather big" would be what you'd say if you were highlighting a problem. For example "My car's OK but it's rather big. Maybe we should take yours? It's smaller so it'll be easier to find a parking space."
In your sentence, the speaker is stressing a positive quality of the room. The guests would presumably prefer to have a room each, so the speaker is emphasising the fact that the room is big enough for two people to share. The size of the room is something positive, so 'rather' would be wrong here.
NB Note about British English. The modifier 'quite' means 'fairly' i.e. not very. The room in question is not very big - it's merely big enough for two people to share ( according to the speaker, anyway).