I am Canadian so maybe I can help. No, the additive is not automatically put in all the gear oils. You should get the additive.
Second - the spare tire rod - mine was in bad shape as well, I just left all of that off the truck and through the spare in the box. Gotta love Canadian winters

 

Just thought I'd update this since I finally had time.

I changed the rear dif oil using the oil I've shown in the first picture and picked up the LSD additive from the dealer and added almost the entire bottle.

As for the rod, I ended up cutting the existing one and reusing it. It's not as long as it was since I cut it, but I just drilled a new hole so the cotter pin would fit through.

Since I have the 3 inch body lift on the truck the original area to remove the tire was now blocked by the rear bumper, so by making it shorter I drilled a hole in the plastic part of the license plate holder so I can fit the extension rod through. The bar I reused is wobbly, but still works fine. Definitely a rough fix, but it works and didn't need to get another bar.

Thanks