Originally Posted by YarnMommy
....but what is the deal with the discrepancy between the rows and stitches?
Could you specify what you mean by the above? Are you asking why your get a different number of rows per inch than you get stitches per inch?
If so, this is because knit stitches are rectangular, not square. Depending on your stitch pattern and your tension, stitches may be wider than they are tall or the reverse.
If your concern is that you cannot match both vertical and horizontal gauge at the same time, I know that happens to some people. It is generally suggested that you aim for horizontal (number of stitches wide) gauge being correct and adapt the length as needed by knitting more or fewer rows to achieve the right fit.
In general gauge for scarves need not be absolute but you should also keep in mind that gauge is always based on final size after washing and blocking. I suggest you block your swatches a little before measuring gauge and make sure your swatch is larger than 4" x 4" for accuracy.
As for K1 versus k1, they are identical.