Fire Imps require a target space of at least four vertical air spaces and three horizontal air spaces to teleport into a location. Despite this, they only need three vertical air spaces and two horizontal ones to spawn.
Fire Imps spawn more frequently as long as there are less than four other enemies on the screen.
The Fire Imp can be stunlocked with many different minions, as their repeated attacks prevent it from firing.
The Fire Imps dropping the Plumber's Hat may be a reference to Mario's ability to shoot fireballs when getting a Fire Flower power-up, similar to the Burning Spheres that Fire Imps shoot. This is further supported by the Obsidian Rose that they drop, which references the Fire Flower power-up.