Have you moved the car, driven it? The way the suspension works, it will be in a slightly raised position when you put it back down on the ground. Roll the car a couple of times back and forward will allow it to settle to normal.
Otherwise, it should drop straight to the intended ride height. Maybe you already had low springs.
Well, a quick Google search revealed the following for DB1165 pads:
SUIT NISSAN BLUEBIRD U12 ZX,ZXE EFI ENGINE 1989 ON
U13 2.0L ENGINE 1993 ON
U14 1996 ON
Generally, Skylines use DB1170 pads in front, DB1220 rear.
White smoke on a cold start is more than likely water vapour condensing in the cooler outside air (the compustion process produces water, amongts other things).
No. The ratio of the front diff is the same as the ratio of the rear diff. Otherwise, the front and rear axles would be driven at different speeds.
What funky means is that the speedo drive gear needs to be changed (as I have just done after I put a Stagea diff set @4.083 in my GTS4 - GT-R drive gear replaced GTS4 drive gear)
GT-R = 4.111, GTS4 = 4.375
Offset = backspace - (width / 2) - which is what you have calculated.
The "width" of the rim is usually the internal rim width (where the tyres sit in). You can only measure the backspace to the outside of the rim. Probably take off 10mm for the thickness of the rim wall.
That should bring it down to 39mm, which is pretty close to a stock 38 offset.
Some rims now have the offset cast into the rim, along with the width and diameter - have a close look.