Ok, here's a stupid question. If you use the Togglers, do you hang the picture directly on the toggle or do you still need the old nail and hook?
If so, how do you attach the nail and hook to the toggler? Or does the toggler stick out enough from the wall to hang the picture wire on it instead of being flush with the wall? I'm a newbie with this sort of thing.

Not a stupid question at all. Most of these drywall anchors require you to tighten the screw to work which won't leave any portion of the screw available to hang a wire on. I can't find a picture of one, but there are hangers made with holes in them that you put the drywall anchor screw through and then tighten the screw. These anchors are really for things like towel bars, shelves, toilet paper holders, etc. There are nail based picture hangers that work fine.

anything with real weight needs to be in a stud or in blocking. Screw a sheet of plywood to your studs and then you can screw anywhere you want into that. Paint the plywood to match drywall or use some stained boards if you want that look.