I have 118,000 miles on the truck. The trans shifts to second and maybe 3rd after you come to the first stop when cold, then is fine. Is the trans toast?

Dealer rebuilt rear + axles at 60,000 miles all new bearings and seals. Now noisy again from rear only. I want limited slip. Is a 4x4 rear the same size and will be a simple swap? Or if rebuilt can it be made limited slip?