Hello

I have been given a Yard King, 22hp, Model 52161X89A, SN: 7405807592N00182, built in 1999, and am trying to get in running order.
The engine now runs good but I am having problems with the hydrostatic transmission. It is slow to respond forward and even slower in reverse.
I found a plastic reservoir on the transmission, it was empty. Next to it is a in-trans fill plug, this is full.
My questions are: 1) What is the plastic reservoir for? 2) What is the fill plug for? 3) Would a lack of fluid cause slow movement in reverse? 4) Where can I get good diagrams for my Yard King?

Thank you for your time