The Arkham Knight HQ is divided to two areas; one is in the ventilation shaft while the other is the actual HQ itself. The ventilation shaft is accessible through the former Killinger Dept Store front in the lower streets while the other HQ is located on top of the Cale-Anderson Pharmaceuticals Building.
"With a fluffy white coat and ears standing tall, what burrowed the hole in which Alice did fall?"
In the Ventilation Shaft LV04 Maintenance Sector, there's a shop to the south with mannequins wearing creepy masks. Scan them to solve the riddle.
"Vengeance burns darkly inside the betrayed, as they stare at reminders of debts unpaid."
In the main HQ, west wing. Look for a pile of militia equipment crates. Beside that is a wall of photos. Scan it to solve the riddle.
"A psychotic doctor who caught the fear bug, the fruits of his research: a powerful drug."
In the main HQ, south wing. Look for an enclosed room crawling with bugs. Scan it to solve the riddle.