1. About an 1" should be enough to keep the studs and insulation from contacting the wall and soaking up any water that may condense on the wall. Also since the wall probably has bows in it, this will keep your stud wall straight. Run a chalk line on the floor all the way around to get your walls straight and square as possible. Then drop a string and weight from the ceiling to mark the corners and chalk line the joists. On the sides parallel to joists, run a string line along the top to line the top and bottom up.
2. Regular fiberglass r-13 insulation with a kraft paper face towards the interior of the basement should be fine. A plastic moisture barrier on the concrete wall from the floor to ground level may be allright but probably not necessary in your locale unless you have moisture bleeding through or condensing on the wall. Control inside humidity with a dehumidifier.
3. Anchors or power nail the bottom plate is a matter of choice. Adhesive would probably hold though. Main thing is to stop any lateral movement. I have a .22 caliber power nailer but have found (depending upon the hardness of the concrete) that I can take the same power concrete nails (with the plastic spacer) and hammer them through the plate and then give them one hard whack (only one) with a 2 lb. hammer and drive them in just as good and quicker than messing with and reloading the power nailer. Every few feet should be enough.
4. I like this site when it isn't being hacked by hackers.