Of course a woman would usually only run a business that is either compatible with her caste or which she is not forbidden to run because it's the exclusive preserve of another caste. So for example, a FW of the Caste of Slavers would usually run a Slaver's House, a FW of the caste of Physicians would usually run a Physician's practice, a FW of the caste of Merchants would run some sort of commercial enterprise that is not the preserve of another caste. Being a merchant probably gives a FW the broadest scope to run a business because she can do anything that doesn't specifically belong to another caste.
Very true! Goreans were specialists and each caste zealously protected their "territory". This held true even within the caste itself. I don't have the exact quote (I just read it in either Rogue or Guardsman) that within the metal workers caste there were those that obtained the metals and prepped them, but couldn't fashion it into anything; there were those that could make collars but wouldn't dream of make a sword.