My Sears riding mower w/automatic trans ( hydro gear transaxle) was making noise, whining and the brake was grabbing. I also had problems going up hill w/o stalling too. I have changed oil & gas, plugs and fuel filter to solve power problem. I took off the back section to check the transaxle, and discovered the actuating arm for the brake was not releasing completely.
1. Is there and adjustment for this are? It has a castle nut, and a cotter pin.

2. what sort of oil goes in it? I thought maybe it was leaking out of the vent cap - the previous owner or service man put a rubber hose extension on it...
Thanks!

As for question #1: you really don't need any kind of lubricant on the linkage. You do however need to clean the rust off the arm to make sure it can move back and forth without sticking. When you take it off to clean it make sure that the two studs (for a lack of a better name) that go into that housing move freely. The metal pins and an aluminum housing tend to make corrosion. Just pull them out and do a little sanding on them too. Put the linkage all back together and tighten that castle nut until there is some resistance when you push the mower back and forth. Then back it off until it starts moving freely again. Your brakes should be working fine then.