Gidday Graeme, my thoughts as follows... others may differ...
(1) What ever hand you are comfortable winding a fly reel with. Technically speaking you are supposed to use the opposite hand to which you cast with. I don't. I cast with my right and reel in with my right. I pass the rod to my left hand to fight fish. Bad form apparently, but works for me.
(2) There some excellent cheap fly reels on the market these days that are of great quality. I personally wouldn't bother with an Alvey. Check out some of the Redingtons. 10wt is a good choice for what you are doing.
(3) A full Intermediate line would best suit the fishing situation you described.
(4) Yes, learn a good joining knot like the Slim Beauty and construct staged leaders that might be 40lb/25lb/16lb or similar.
(5) Screens don't help... go fishing
(6) Rod & Reel I suppose or Westgate Hunting and Fishing.