The most natural is "China has a fifth of the world's population" or "The Chinese are a fifth of the world's population."
"Chinese" is wrong. "The Chinese" is correct.
(p.152 - unit 7C - English Grammar in Use 4th ed. by Murphy (Cambridge). A PDF is probably available on the internet.)
"count for" is incorrect.
"account for" is correct.
New Oxford American Dictionary
count for
• (count for) be worth (a specified amount): he has no power base and his views count for little.
account for
2 supply or make up (a specified amount or proportion): social security accounts for about a third of total public spending.