Dear Ms. Lena,
With respect to your initial question can we add feilds in warehouse task - Yes with extension feild using key user adaptation.
with respect to your second question - On-hand stock is usually checked in stock overview page and this page displays data from various BO(business object) from backend. So with standard method(adaptation) will not be possible to show on-hand stock in warehouse task.
you will have to think of some custom solution to full-fill your requirement
Regards
Leo