Here's his story.
Freddy can manipulate the dreamscape as he desires. He will often take the normal dream and twist it in strange and dangerous ways adding hazards and other obstacles to confuse and frustrate his victims. Treat him as a DM creating a dungeon.
Freddy cannot be permanently harmed nor destroyed in the Dreamworld. He takes damage normally; if the dreamer has an assault rifle in his dream it can do damage to Freddy, if Freddy summons a vat of acid and falls into it he is damaged, if the dreamer slashes him with a machete he takes damage. However...
Any damage done to Freddy is repaired if he takes but a single round to rest and do no other action or moves. If he is brought to zero hit points or lower he appears to die. He then reforms in a new body 3d6 rounds later in the location of his choice.
If a DM rules a character is in danger of falling asleep he can call for Constitution checks to stay awake every 15 to 20 minutes. Each roll is at a cumulative 1 penalty until the character falls into a coma-like dream-state. At first they will not realize they are asleep and the characters are now at the mercy of Freddy's depredations as he attempts to play upon their fears.
Fear Checks in the Dreamworld
Fear is the key to Freddy's killing sprees. He cannot damage the dreamers until he has made them afraid. He manipulates the dream, often based on their fears or desires he senses in the dream. He can manipulate the dream environment (recreating his boiler room is a favorite), alter their bodies, mutilate himself, kill dream versions of their loved ones, etc. His power to do this is limited only by the DM's imagination. This manipulation causes a dreamer to make Saving throws or be afraid. Each Saving throw failed by a character gives Freddy the ability to damage him or her. The more failed Saving throws the more damage he can do.
After the first failed Saving throw he can do 1d4 damage to a dreamer, the second gives him 1d6, the third 1d8, and so on up to a maximum of 1d12 damage. When a Saving throw is successful the dreamer is less afraid and the damage is reduced back down the scale in the same way.
The form of the damage done can be as simple as slashing the victim with his glove or as complicated as pulling the veins from their body and using their dream body as a puppet. The DM has huge amount of fiat in this to simulate Freddy's control of the dream. This is how he can appear as a snake or a tv with arms. The form of attack is just flavor to get damage done.
If the dreamer fails his fear Saving throw he is at a disadvantage: all of the dreamer's combat rolls with Freddy (except damage) are at a 2 penalty and Freddy has initiative over the frightened dreamer although he will often let them go first and do their best to damage him in order to show them how helpless they are when it does not stop him.
Once the fear Saving throw is made and damage is figured out combat proceeds as normal. Initiative, attacks, Saving throws: all are normal combat procedures. Damage done by dreamers is normal damage based on what they have with them in their dream or what they can improvise.
Once the victim reaches zero hit points or less Freddy has free reign to kill him in the goriest and imaginative way possible. He may keep them alive for a few rounds to sadistically enjoy their terror before snuffing them out.
Combat with Freddy in the dreamworld is a losing strategy. The dreamers must stay awake or find a way to destroy Freddy outside the dreams.
Once locked into the coma-state that traps a dreamer in the dream he or she can attempt to wake up and escape. The dreamer must make three Saving throws. They take up an entire round, no movement or other actions, and do not have to be made immediately one after another. On the third Saving throw they instantly awake. Wounds acquired in the dream are retained in the waking world as well are small objects the dreamer was holding.
A dreamer can be awakened by those outside the dream if at least 1 hit point of damage is done to the coma-like dreamer. This pain instantly awakens the dreamer.
Freddy can be pulled from the dreamworld into the real world if he is grappled by a dreamer and that dreamer is awakened.
Once in the real world he has no power to manipulate reality. He will attack primarily with his bladed glove (1d6) twice a round. He is not above picking up other weapons and using them.
Killing him in the real world has so far not permanently killed him. He will return to the dreamworld to wait for more victims.
This was a difficult write-up for me, especially working up the mechanics of the dream combat and Freddy's omnipotence in dreams. I tried to keep it within normal game mechanics without too much complication especially with Freddy's abilities to cause endless varieties of damage and illusions. The potential for mechanics bloat is amazing. Hopefully I accomplished avoiding this with the fear Saving throw effect mechanic. Running Freddy will call for quick decisions and a lot of imagination on the DM's part. Enjoy.