To "fir out" is to place strips of wood on top of other strips of wood in this case the studs. The studs are installed vertical. The firring strips would be installed perpendicular/horizontal to the studs and spaced every 16" on center. Making sure that the seam/juncture of the lower cement board and upper cement board have substantial firring behind it. This may require two firring strips at the seam/juncture location if using 1X2 firring.
Cement board is typically 1/2" in thickness but the quality control isn't that good these days. Fiber cement board is typically 7/16" thick even though they call it 1/2" also. Go figure.
Yes you can feather the cement board/drywall juncture but use thinset to do so. Probably shouldn't shim the drywall and create a curve you don't want. Filling it later is better in my thinking.
I would install the seam tape over the seams and wait until I was spreading the thinset to set the tile to fill the seams at that time. The cement board/drywall juncture may require a little advance fill.