When determining the RS and WS of the work, essentially it just asking you which side will be seen and which side will not. The side that will be seen is the RS, the side that will not is the WS. For some patterns it doesn't matter (ie. garter stitch). In others it is very important (ie stockinette stitch).
As for the purlwise indication, it means that you should insert the needle into the next stitch as if you were going to purl it. However, instead of wrapping the yarn and actually making a purl stitch, you are simply going to pull the stitch off the left needle and onto the right needle.
As for turning the work, you are going to turn the work around as if you had hit the end of a row. Eventhough you will be in the middle of a row.
It looks to me like you are doing a short row. There is a video under the videos tab at the top of this website that shows how to do a short row. The technique you are doing is called a wrap and turn, or it will be abbreviated as W&T for short.
OTN: Jeckyl and Hyde Hat, Shetland Shortwrap( )
FO: Lacey Stole, Library Capelet, Dead Fish Hat, Tree Bark Scarf