Aggressive geometry – Flattening and dualizing template of a family of curves

I'm trying to see if the following things are valid: a family of curves $ pi: X rightarrow S $ or $ pi $ is clean and flat and diets $ X $ and $ S $ are arbitrary is it true that the sheaf of relative splitting exists? In addition, I would like to know if you are considering a vector bundle $ E $ sure $ X $ and flat $ S $, the tensor product of $ E $ with the sheaf in relative duel is flat. Thank you for your time.