lots of questions there man!
ok...because your car is auto i think that you may have a few dramas getting really short diff gears and no auto mods.
pre-electronics autos work directly off oil pressure that is set by a governer, that is directly attached to the output shaft, and if you make the output shaft spin faster for a given road speed (by putting in short gears) i think you would find your auto would change up gears too early, even under full throttle.
the borg warner 35 boxes (which i think yours is?) have a cable that runs to the throttle (at least on the carby models) which depending on its adjustment can make the shifts higher and harder, or lower and softer - you could maybe adjust this cable to compensate a little for the diff gears, but i think driveability in normal conditions and gearbox life would suffer.
you do need to change the little gear in the transucer on the box, but some people reckon there is a little screw you can adjust in the top of the XD instrument panels - though i assume you have a digital dash being an EFi car?
this is all theroetical however, and would depend entirely on the diff gears you choose - the more different from stock the more potential for probs you have though.
find out what ratio your diff is stock, and what rpms you are doing @ 100km/h, then decide what is the most rpm you would want to put up with at this speed, from that we can work out what the lowest ratio diff you can have is, IE: (guessing)
2.77 stock, and say...1600rpm@100
and we will assume you want to rev it at 2200 on the freeway.
2.77/1600*2200 = 3.808
so you would get either a 3.7 or a 3.9 diff, depending on if you wanted to go a little under or over your taget figure. HOWEVER to fit anything above a 2.77 to a 2.77 diff center will require a spacer to be machined up and longer anticlockwise threaded bolts of sufficient strength to be found - WBT56 is not keen on this idea, and i have to say i would rather not do it either, but i have a 3.9 diff built using this method and so far its coped with my thrashing the guts out of it at willowbank, archerfield and QLD raceway, along with general irresponsible driving on the street with 200hp at the wheels, no worries.
if i was you (and had a 2.77 center) i would source a 2.92 or shorter LSD center from a wreckers or something, and get someone to rebuild it with the gears you want in it, either sourcing the gears you want from another wreckers or whatever, or getting the shop to supply gears. i think they are about $270 for lapped gears second hand, but im not sure at all on that point. maybe check ebay and see if there is anything there you can use - Aussie R31 skylines are usefull for their 3.7 (manual) or 3.9 (auto) diff gears - if you can get them at the right price, and find them!
dont bother changing your gears if you arent going to get an LSD - i would rather a 3.08LSD than a 3.9 open diff!!!!