#1 You're talking about the door frame. Four pieces of 3/4"X2" (or whatever dimensions) wood make the frame of the door. The plywood had to attach to it somehow. So, on the backside of the frame(b4 its glued together) I cut away a 3/4" piece (3/8" deep which is half the thickness of the frame) all the way around. This creates a recess for the plywood to fit into much like a picture frame.
#2 I'm not sure if you're talking about the hood or stand? For the stand, neither. I cut the front corners at 45 degree angles so it wouldn't require corner moulding to hide the butt ends. If you're going to put corner moulding (trim) on it, it won't matter except for dimensions. To put the sides overlapping the front and back will make the stand 2X's the thickness of the plywood your using wider than the front (and back) piece. If you overlap the sides with the front and back, then the stand will only be as wide (long) as the front and back piece.
For the hood, it doesn't matter since I covered the corners with moulding. As for the top, it covers all so when looking at it, all you see is the top butted against the trim. I actually used Luan plywood. That's the real thin stuff, 4mm thickness I think? Look through the pile b/c it varies in shades.
HTH, if not, ask more questions!