Hi and welcome to the forum!
When changing the hydraulic oil, it is very difficult to get every last drop of oil out of the system, and for the most part nobody bothers, unless you have had a catastrophic failure of a pump or a motor. Not only will there be some oil in your cooler, the cylinders and hydrostatic drive will also have some in them too.
What some people do is connect a hose to one of the aux. ports and run the machine at idle while actuating the aux. control, allowing the machine to pump itself out into a bucket. When the flow begins to spit air, shut the machine off and refill with fresh fluid.
More importantly, change the hydraulic filter.
With respect to how much fluid your system holds, somebody else will have to chime in on that. I know our 773 takes nearly a whole 5 gallon / 20 liter pail to refill it. I am thinking yours is probably near the same.
Hope this helps - SR