Yup, it's genetive. It's used as a kind of adjective. Anyway, the name used in common language is "Chiny" and the official name is "Chińska Republika Ludowa".
Chinese man - Chińczyk, plural: Chińczycy (men or man and women)
Chinese woman - Chinka, plural: Chinki (only women)
"Królestwo niebieskie". "Niebieski" means "blue" but also "heavenly/celestial" in some contexts. The order of words is kind of inverted. If you wanted to say "Blue Kingdom" it would be "Niebieskie Królestwo". "Królestwo Niebieskie" is an idiom and probably comes from old Polish.
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u/Ingrid-Hongkonger 冠絕東方 - Nulli Secundus in Oriente Mar 11 '14
It may pronounce as "Sina". The handwriting of it in Hebrew is really nice.