When your illuminated by the moon your true form is reveled to everyone that can see you.  The true appearance of your face and head is determined by your elemental affinity.  When not illuminated by the moonlight you appear human or elven (depending on what you were in life).  You know the thaumaturgy cantrip. Once you reach 3rd level you can cast 'find steed' once per long rest. The mount conjured is considered a fiend creature. Additionally the steed can be stored in the Nine Hells as an action can be stored and can be retrieved as a bonus action.  Any mount or vehicle that this Ghost Rider kills or owns that can't fly can be used as a summon for this spell.

As a bonus action you can summon from the Nine Hells long chain that can be used as a whip and counts as a natural weapon.  You can use an action to attack with it.  This chain counts as magical and silvered for the purposes of getting over resistances.  If you hit with it, you deal 1d6 damage of your chosen element.

As an action you can choose to wreathe a creature in your chain forcing them to make a strength saving throw against your spell save DC if you have one.  If not then the save is 8 + your proficiency bonus + your constitution modifier. On a failure the target is restricted and must succeed an acrobatics or athletics check against your save DC at the start of each of their turns or remain restricted.  While you have a creature restricted you can't use the chains for anything else.  You can return the chains to the Nine Hells as a bonus action.

This weapon's damage increases by 1d6 when you reach 5th level (2d6), 11th level (3d6), and 17th level (4d6).

You also get a weakness corresponding to your elemental affinity.

You have vulnerability to bludgeoning, piercing, and slashing damage from silvered weapons. 

You have advantage on saving throws against being charmed, and magic can’t put you to sleep.

You don’t need to sleep. Instead, you meditate deeply, remaining semiconscious, for 4 hours a day. While meditating, you can dream after a fashion; such dreams are actually mental exercises that have become reflexive through years of practice. After resting in this way, you gain the same benefit that a human does from 8 hours of sleep.

Your base walking speed is 30 feet.

You can speak, read, and write Common and one extra language of your choice. Humans typically learn the languages of other peoples they deal with, including obscure dialects.

As the old saying goes, two is company and three is a crowd. Your body is already shared with the demon bound to you which protects you against others who might seek to inhabit your body. At 1st level, you gain advantage on wisdom saves and saves against being controlled.

You gain dark vision up to 60ft.

Ghost Riders don't need to breathe.