What I generally do when I hit HFS and have no idea where the pits are is dig out a small room nearby with a bed and food stockpile in it. Assign a miner to the bed. When he goes to sleep wall the miner in with constructed walls. After that the miner in there is free to mine away at the adamantine with out endangerouring your whole fort. I usually try to take a direct path from that miners room to where I suspect the pits are, keep the poor locked up miner digging until you hit the pits. When you do, the demons there will kill him pretty much instantly but atleast you now know where the pits are and the type of demons in them without endangering your fort. If they aren't spirits of fire I will probably proceed to digging a hole in the roof of the pit for above and then funnel magma into the pits (through the newly created hole) killing all demons inside. If they are spirits of fire, there are two things you can do to avoid the destruction of your fort:
a)Train an army of melee weapon champions(I would say that 15 is probably enough) and wall them in with a miner then dig to the spirits of fire using the same technique as above. There you should try to find a sharp corner where you can hide your champs out of range from the deadly fireballs. When the spirits of fire come around the corner, they will be too close to the warriors to let any fireballs off and will engage them in hand to hand. Your champions should win in a battle as Spirits aren't that powerful close up.
or
b) Just take the FPS hit assoiciated with the invisible demons and never touch the pit again. You can mine around it for adamanite, but make sure not to hit the pit.
Oh and another thing you should know is that the pits are always on the bottom 4 or 5 z-levels. The adamanite itself will go from the second to last z-level all the way up to about the 10th z-level from the bottom.