Well, the sealing is easy enough, you can lock doors and/or floodgates with a lever throw. Doors are instant but need a nearby wall, while floodgates take 100 tick delay, and can be lined up without nearby walls, for wider areas. Pressure plates directly beside the doorways can be triggered at 2/7 water/magma, causing them to close as soon as fluids get out of hand (and much faster than a lever-dependent system), and doors can be made to close when a creature steps on them, keeping invaders out as well.
As for obsidian casting, this is also possible but more challenging. To really achieve it, you'll need at least 2 layers between each level, one for magma and one for water. On the quarantine section, it would have a few hatches along the floor, and hatches along the entire ceiling. Upon triggering, then the hatch should open and magma floods in from below via intense pressure (those auto-sealing doors should keep any extra flow in check). Some well-placed pumps should allow you to pressurize specifically. Then, after a few ticks, long enough to flood the room with magma, the ceiling hatches should open and drop water down, casting obsidian. For this reason, it's important that the magma pressure be specific, so that the magma doesn't flow up and cast the ceiling. The water should fall, not the magma rising. The water doesn't need to be under pressure, but it likely will be anyway, it won't really matter.
On another note, if you're trying to isolate a specific dwarf, either to contain a syndrome or to keep the dwarf away from a syndrome, having a manager-order lever will get him into a room quickly. I've also been testing a design for extremely rough closing doors, which involves using several layers above the door for design, but will allow you to drop a natural block wall to seal a doorway tight.