Some answers:
The stem is the vertical tube that is pressed into the lower clamp, passes thru the frame's "headstock" and is then topped off with the top clamp (fastened by screw on nuts). The reason he may have used the stock 400 stem is due to the length difference, but again, the 600 stem could be pressed out a bit, then trimmed with All Balls bearings mated to take up the outside diameter differences.
A Cognito hub makes things much easier. No fab, stock 600 axle, rotors, calipers, wheel bearings. Cognito also makes adjustable triple trees (the upper and lower clamps plus a stem) to convert your 600 forks onto a 400 frame. They're pricey, but they are complete, bolt-on products and beautifully made. Something to consider...
The offset is the distance from the center of the stem (looking down) to the line between the fork tube centers (again, looking down). This distance is the offset, and your 600 probably has a smaller offset compared to the stock 400. That was the reference made in an earlier post about effects of steering geometry. While mathematically its true, I suspect most riders don't suffer the negligible effect.
A steering damper is not required for street or track, but they are a very good investment when you modify steering geometry, especially for newer riders. But it's mostly a 50/50 opinion on their need.
Your forks have very good springs already, so you probably don't want progressive rate springs, but instead stick with single rates. Your forks also have more adjustment to them than the stock 400 forks. Again, use YouTube and search " 1993 CBR fork adjustments"