I've been looking for Hellforges in the Underworld, but I haven't had any luck. I searched ALL of the towers on the right side of the Underworld, but I haven't seen any. I read on somewhere (not a wiki) that said to look for Hellforges in the Dungeon. Is this true?
You can't find Hellforges in a dungeon directly, but if you manage to find one outside the dungeon wall (because dungeons can reach the Underworld) you can mine your way out and use it. Or, you can just keep looking in the Underworld or make a new world to get one.
Dungeons never extend directly into The Underworld, although if your dungeon comes close you may find a Hellforge at the point where it does. This is much less likely than finding one in the Underworld proper.
Bear in mind that there could potentially be a Hellforge in an underworld building submerged in lava, if you can't find any easily accessible ones on the surface.