Take a look at the Norton also, Machine Design, the explanations and methodology are easier to follow
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Yes, please don’t be malicious to China.
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No.
This picture shows that every tooth on 1 pulley won’t touch every tooth on the other pulley.
However, you might still think that 15:36 is a good ratio for spreading grease, since maybe excess grease from 1 tooth can still somehow make it’s way to every other tooth. But no!
The tooth count MUST be coprime. The easiest way to realize this, is by seeing that 15 and 36 have a common factor of 3. Let’s paint the teeth on both of our pulleys in 3 different colors, alternating in the same order. (Red, blue, green, red, blue, green, etc.)
It’s pretty easy to visualize that if we first connect the gears so that matching colors touch, it’ll always remain this way. Red teeth on 1 pulley will only touch the red teeth on the other pulley! So grease / imperfections will be balanced evenly within these 3 color groups, but not entirely throughout the system.
Conclusion: the smaller the common factor, the less groups, and the more evenly we distribute wear and grease! And the smallest common factor one can hope for is 1, so a pair of gears with coprime tooth count is preferred 
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I would like to add here that if you want to avoid undercutting of the gears, the minimal number of teeth on the pinion should be 17, would be a good thing to consider for the gearbox makers here.
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This is same in any country. Can have good or bad manufacturing. It not based on country at all. This ignorant.
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