1) Can I somehow forbid an item from use? Or put an item on auto-dump? (For example, if I don't want diorite or some rock, is there a way to make sure that it is dumped as soon as it is mined? Or forbidden to made into anything in workshops?
Check out {z} screen and the stone screen. Make the stone you don't want to use a economical stone ( red-colored ). You can turn ore on for stone usage if you want so from there.
2) Rat remains, lizard remains, other crappy remains. I currently have these being dumped outside my fort in a corpse pile. Do they ever go away? At what rate do they decompose? Is dumping them an more preferable than piling them? Also, often times my dwarfs won't move rat remains - what the hell is wrong with them and why are they lazy?
Are the remains outside? You'll have to permit them to take refuse from outside, o>r>o>v, you might have to set refuse gathering on, which's in the same menu. They decomposes slowly, I prefer to set them to be dumped using o>r>k, they don't stinks up, so you'll be fine.
3) I still don't really understand cave-ins, even after reading the wiki and other explanations. How does a room or structure become disconnected from all support?
By not being connected at N/S/W/E by walls, floors, supports, ramps, fortifications. Walls and supports holds things below and above them. If any part of structure aren't connected in those way, it'll cave in.
4) In my current fortress, I have yet to find any lignite or bit-coal, but I have found some magma about 8 levels down from where I currently am. Should I set up smelters for coal in the meantime, or just go straight for the magma, and how would I go about this? I haven't worked with magma yet, any advice on how not to melt the universe would be appreciated.
Go straight for magma, I'd say, and make sure you never have a doorway straight into it on same level. Channel out a few spots for your workshops to get magma ( all the better if the impassable squares can cover them ), then connect them by mining. Take any ores out, and preferrably all stones so you can either dump them properly later or use it up. Then finally, smooth the wall between magma and the rest of the tunnel (prettier if you smooth all of it, but not needed ) and make sure ramps are still there ( it won't get in the way of powering things ) and carve fortification in a corner. Wait for it all to fill up past 4/7 (The magma works won't run with less ) and build the shops on top of the channel-holes.