My friend gave me an easy pattern from memory and told me to cast on 39 sts, knit the first row, and K1, P1, K1 every other row. When she finally found her pattern, the second row said to P1, K1, P1. Does it matter whether you use a knit stitch or a purl st to begin and end that second row? Since the first row begins and ends with a knit stitch, it would seem okay to me to begin and end that second row with a knit stitch. But maybe it looks better to begin and end with a purl st. Does it matter?

I've heard somewhere that you should slip the first or last stitch (or maybe it was both sts) when knitting a scarf to get an attractive edge. Is that true?

As long as you were consistent it should not matter.
You can slip the last stitch for a neat edge