Chinese ( adjective) - Chinese boys ,Chinese architecture, Chinese premier,etc.
Chinese( noun) - The Chinese ( refers to people).
China's (possessive) - China's boundaries, China's economy. China's army,etc.
Of China - Again used to denote possession - The boundaries of China, the literacy rate of China
Yes, "China" means " Chinese" in the examples you have mentioned above.
'china' is also a synonymous reference to cutlery,Chinese ceramics and tableware.