What determines the thickness of Cornea?
The corneal thickness is genetically programmed. There are multiple genes that induce the final corneal thickness:

USP37, Chromosome 2; 
GPR15, 3;
TIPARP, 3;
CWC27-ADAMTS6, 5;
RXRACOL5A1, 9;
LCN12-PTGDS, 9;
FGF9-SGCG, 13;

and at least 6 other genes.

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other questions had to be asked as separate ones