When quello is used as a pronoun, only the form quello is possible.
When it is used as an adjective, you must follow the same rule used for the articles il/lo. Il -> quel or lo -> quello. The same rule applies to the plural form quei/quegli.
It is both. See: http://de.pons.com/%C3%BCbersetzung?q=paese&l=enit&in=&lf=it
Also see the discussion above.
I'm confused. "In which country do they eat rice?" is a different question from "Do they eat rice in that country?"
The first question ("In which country . . . " requires an answer that names a country where people eat rice. The second ("Do they eat rice in that country?") requires a yes or no answer.
That's a totally different sentence. This one is "Do they eat rice in that country?" Like if someone said, "Andiamo in Cina!" and then another person said "Mangiano riso in quel paese?"
The reason it's "bad english" is because it's lacking the word "in", like dnovinc said above.