PA-44 flight instructor with student reported landing gear malfunctioned when extended resulting in gear not locking and then collapsing during landing.

Narrative

Instructor and student went out to the practice area to do maneuvers. Student performed a power off stall and had the gear locked down and confirmed. After the maneuver; another power off stall was requested; student put the gear down and instructor heard a popping sound; along with a flashing nose gear indicator. Instructor took controls and cycled the gear to see if the gear didn't lock properly; this did not change the outcome. Nose gear seemed to be free falling and the hydraulic pump for the gear was still active and ammeter were constantly going up to 35 amps and back down as if pump was activating. Instructor confirmed by swapping the nose gear light with the main gear light but light was still flashing. Instructor pulled flaps to 45° to confirm as well with the gear warning horn still on. Next instructor attempted to pull G's to lock the gear into place gear still was in a free fall. Instructor ran the emergency gear extension checklist and pulled the manual gear extension. Nose gear was still in free fall and instructor pulled more G's but the gear seemed to hit the extension limit and not lock into place. Instructor attempted to pull more G's but to no avail. Instructor [advised ATC] and did a Runway flyover at 1800ftmsl over Runway XX at ZZZ to check the gear nose gear confirmed free fall and not locked in. Instructor took the landing. Gear collapsed on impact with the Runway. Fuel selectors; mixtures and fuel pumps were cut upon touching down.