Let me try to answer to the "debate whether China has fabricated its GDP in the past". The rest of the question is too broad to be answered properly and should be rephrased.
Jia, Kudamatsu, and Seim (2015) use the methodology of Henderson, Storeygard, and Weil (2012) to corroborate the quality of the provincial growth data by checking if it reflects the growth in nighttime lights observed by satellites. Nighttime lights can be seen as an objective measure of living standards, and therefore its correlation with GDP is indicative of the quality of GDP data. They find such a correlation suggesting that real GDP growth, at least to some extent, reflects improvements in some dimensions of living standards captured by nighttime lights.
- Jia, R., Kudamatsu, M., Seim, D., 2015. Political selection in china:
The complementary roles of connections and performance. Journal of
the European Economic Association 13 (4), 631–668.