Great news! I knew it would work out. Depending on how much trouble it is to do it over again, vs. the price of new cables, I'd look very seriously at replacing those. Since the cables will never slide the same way as when new. They'll always bind, and be prone to rust again. There's nothing wrong with trying to salvage parts, but you might be spinning your wheels there with soaking. All new cables, springs, and probably the hardware also, is probably the best way to go. But it never hurts to try. They'll certainly be better than what you had before. I'm glad to hear you're on the way to getting a handle on that parking brake.
Now for the axle bearing, and seal. You'll want to do both sides. If you have to pull the axle out of one side, its a small step to do the other. Assuming it's like a cars differential, it would have to be opened to release the axle clips.