Use a UDT type fluid. I personally use Traveler brand like this but there are a bunch of options that are similar. Just don’t use a fluid that is “303” fluid of any type - it is supposedly junk these days.
The fluid is probably milky due to water getting into the transmission through the gear shift levers. I keep mine covered and no longer have milky colored fluid.
There are drains on the bottom of the transmission and lower drains on the lower inside wall of the rear wheel drive enclosures. They all drain the transmission sump that is also the rear axle lubricant and the hydraulic fluid pumped by the tractor engine mounted pump.
There is a screen strainer inside the transmission at the fluid suction line. It is removed from the opposite side of the tractor as the pump and suction line. It is in the same position but opposite side as the suction line connection point on the transmission case. There is a cover with two bolts and a bump. There are o-ring(s?) and a spring under the cover so be expecting them to fall out. You will probably have to grab the end of the screen with small needle nose pliers to get it to slide out. If the muffler and tailpipe are down there, they are in the way a little bit. Screen can be cleaned unless it is damaged or missing.
Since you have a DT you need to change the fluid in the front axle also and can use the same UDT type oil.
Since you asked about the FEL it may use the tractor sump as the fluid source or it could use a separate pump mounted at the front of the tractor and use a fluid reservoir on the FEL, usually in the FEL tower. Follow the hoses from the FEL valve to see where they go.
If you have other questions about it, just ask.