Hello sir,
Congratulations on your son's success.
The authorities have not officially declared any institution wise cut off lists yet for 2019 but using previous years data we can predict his chances.
According to previous years cut off trends your son has very high chances of getting mechanical design at IIT Bombay ( last year cut off was 600 score/general category),  Mechanical engineering at IIT BHU ( cut off was 747/general category),  mechanical design at IIT Delhi ( cut off was 725 score) amd mechanical design at IIT Madras ( cut off score was 835).
In general the fee varies from one IIT to another. However, the difference will not be that much big to bother, It is around 30k-45k / semester ( excluding scholarships)

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