The best way to dig out a large, multilevel chamber is to first designate the entire thing to be made into staircases (top level down stairs, bottom level up stairs, everything else up/down stairs), then let it be dug out. This will give your dwarves access to everywhere in the chamber, including the walls, for smoothing and engraving. Once that's done, designate the whole top layer to be channeled. The dwarves will do it from below, and the staircases will support the top layer, so no caveins will occur even when your miners dig a checkerboard pattern. Then, once that's done, designate the next level for channeling, let it be done, and repeat until you're at the bottom. At that point, simply designate the room full of unconnected up stairs for up stair removal, and in the end, you'll have a complete, clear, open space, several z-levels high, and all with no danger of caveins and relative ease of designation.
To get magma out of a volcano, designate part of the volcano's wall to be dug out. Watch it. As soon as a miner is working on it, designate several other places for digging elsewhere far away. The idea is to make it so that as soon as the volcano wall is breached, the miner sees another dig job waiting, and goes to do it, sending them running away from the inevitable wall of magma coming their way. They will almost always outrun the flow, in my experience. If you'd like, you could even cancel the "extra" dig job after your miner is out of harm's way, though if you've got multiple miners the others might get to the dig zone first and so cause trouble if you really didn't want that wall dug, so make sure it's somewhere unimportant.