I think the rise of «на кухні» («на кухне») in Ukrainian (Russian) is connected to the fact that a kitchen is sort of an "area" in your apartment or house where you engage in cooking/eating activities.
There aren't any other rooms that use "на", I think (there is attic, though,— «горище» in Ukranian)
In English language: Yes, but it makes an emphasis on "his things"( for example if you ask "What is there in his room?") "His things are in the room" is more general.
На Українской мове: Так,можливо,але це робить акцент на "his things" (на приклад, коли ми запитуємо "Що у кімнаті?") "His things are in the room" є більше загальним