A. As far as I know, there's not a simple way to see what a lever's linked to. I generally build my levers out of a particular stone color to remind me what it's for. I use a basalt lever for my drawbridge control, a microcline lever for my water intake floodgate, a bauxite lever for my lava pump, etc.
If you don't want to do this for whatever reason, Toady recently added a feature that lets you add "notes" (shift-n) in fortress mode. This is a sign that's only visible to the user (not your dwarves) in which you can enter any text you want. You can put a note on or near your levers indicating what they control.
There is one complicated pain-in-the-ass way to find out. With any particular lever, you can link it to more than one thing. So, you highlight the lever with "q" and then create a new task to link the lever to something, then you scroll through the list. Everything in your fortress that you can link the lever to will show up in that list. By the process of elimination, the one mechanism NOT on that list is the one the lever's linked to. You really shouldn't do this though, just color-code or note your levers.
I'm not sure about the pressure plates. Somebody with more pressure plate expertise than myself can tell you.
B. Weapon, cage, and stonefall traps don't need a trigger to work, except for "menacing spikes". If you have ten obsidian swords or a spiked ball in a weapon trap, it will automatically trigger when any non-trapavoiding character walks on the tile containing it. They also trigger when a dwarf or tame animal falls unconscious on that tile. Stone traps work once, then generate a "reload trap" task before they'll function again. Weapon traps work over and over, but occasionally get jammed up with body parts and gore and generate a "clear trap" task before they'll work again.
C. Again, I'm not a pressure plate expert. Somebody else?