I won't tell you what to use in your KE20, but to save you typing into the search field I will try and answer your questions.
The least widest Hilux axle is from a RN10/RN13 1968 to 1972, but I can't tell you what spec diff is in that. The RN25/27 1972-78 diff measures 1370mm hub to hub and has a G series (8 inch) centre. If you want an LSD you have to find a G series one, from typically say a Forerunner or a Surf (import) 1987 to 1998.
If you want disk brakes you have to do what amounts to a custom conversion. Again, search.
Mitch.