Could be a few things, caliper piston stuck, hose collapsed inside creating a one way check valve, (fluid in but not so much out) caliper slides binding due to lack of lubrication. Yes there is supposed to be a special high temp brake grease that keeps the caliper slides from binding. Bent backing plate/caliper mounting bracket. Hard to say without putting my hands and eyes on it personally.
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I second the caliper slide pins not sliding properly.

 

The diff cover can wait until you decide to change the fluid.

 

this.

 

Mine looked like that. I had to replace both front caliper mounts since the slide pins were essentially welded in.