This page is very interesting :
http://www.heicshipslogs.co.uk/logs/h009.htm
Note there were five HEICS ships named Warren Hasting and some were sailing at the same time, so if you want to learn more about the ship your people sailed on, you will need to be clear about which one she was!
This page:
http://www.heicshipslogs.co.uk/encounter.htm#wooo
has further info about WH 2 and 3.