Is it still possible to go from Kazakhstan to China by train?
If I search on the web site of the national railway company Kazakhstan Temir Zholy, I don't find any connections to China.
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There is a train station in Khorgas which is at the border and has a border crossing.
This page here has a map with border crossings in the whole region: Border crossings on the Silk Road
You can take go from Almaty 2 or Astana to Ürümqi by using the Kazakhstan Temir Zholy. From there you can probably reach the rest of China by using the China Railways trains.
I generally use rome2rio to find trains in places where public transport is hard to figure out.