The Martian Manhunter is one of the important members of the Justice League. He can transform into any creature and adapt to any condition.
In Supergirl TV series his role is played by David Harewood? What are his powers or what superpowers does he possess in the TV series?
Arrow Wikia, listed it quite well:
Green Martian physiology: Like all Green Martians, J'onn possesses several incredible powers. Overall, J'onn is an extremely powerful being with even Superman referring to him as "the most powerful being on Earth".
Camouflage: J'onn can blend within the environment by changing the appearance of his form to bend the light waves around him to match with his surroundings making him almost - but not completely invisible.
Density-shifting/Intangibility: As a Green Martian, J'onn is able to move through solid objects (such as walls and doors) or to increase his density to become near-invulnerable. He is able to use this offensively, allowing him to phase through people to cause internal damage or even pull organs out of the body, as he did to Metallo to remove his green Kryptonite infused heart. Invulnerability: J'onn's body is far denser than a human's, but not quite as durable as that of a Kryptonian like Superman, while he is able to make himself more dense. As a Green Martian J'onn is immune to human diseases and illnesses.
Longevity: J'onn's life span is considerably longer than a normal human and likewise ages much slower. Despite being over 300 years old, his health, performance, and natural appearance has remained unchanged.
Shapeshifting: J'onn is able to change his form at will, even on a cellular level, completely altering his physical appearance, allowing him to transform or mimic other people or animals and other creatures. His abilities allowed him to appear with clothing and other wearable items when transformed and retain what he was wearing when in a specific form, such as his Martian Manhunter uniform or the sidearm he uses as Hank Henshaw. However, due to the fact that he was retaining his powers, he couldn't pass the biometrics scan locking mechanism that required Maxwell Lord's fingerprints in order to access through. Also, when posing as Kara, he had trouble walking due the high heel shoes he had in that form.
Malleability: J'onn can stretch and bend his body and limbs. (E.g. into large whips to grab things at great distance).
Accelerated healing factor: Due to his shapeshifting powers, J'onn is able to heal faster than a human would. This caused any wound inflicted on him to glow red and then vanish in minutes, which happened when he was shot with Hank Henshaw's special bullets. He was also able to heal himself soon after being stabbed by Indigo, though it took time for him to recover from it.
- Super strength: J'onn has strength above that of a normal human, as well as aliens like Jemm, although not as strong as a fully-powered Kryptonian. He is able to augment his physical strength by focusing his telekinesis and using it in a tactile way. As shown when fighting a Red Kryptonite-infected Kara, J'onn is able to apparently surpass a Kryptonian's strength when using all of his powers (strength and telekinesis combined); however, it should be noted in his confrontation against Astra, even when J'onn used all of his powers, he was able to put up a fight, but was still ultimately no match for the latter. This is likely because unlike Kara, Astra had full control over all her powers.
Telepathy: J'onn is able to read the minds of other people (except for Kryptonians) communicate with others mentally and projects his thoughts into others, as well as hear others people's conversation psychically. His telepathic powers are shown to be very potent, able to overwhelm the minds of other powerful telepaths.
Mental detection: J'onn can feel and detect the mind of others, as well as their intentions, emotions and mental states. J'onn use this abilities multiple times, as when he sensed Alex Danvers' presence at the D.E.O, knowing Jemm was controlling the mind of the guard the and when he track and detect the location of the White Martian. He can use this to see with his mind like a mental view.
Mental shield: J'onn can telepathically shield himself and others from mental intrusions with enough effort, such as preventing other telepaths from scanning his mind. Doing this for Alex Danvers caused him some discomfort due to the effort and was unable to sustain it when he was wounded.
Mind control: J'onn can control the thoughts and actions of others (except for Kryptonians), implant words in other's mind, as well as to erase or restore and alter the memory of others, reprogram other people's minds and put others to sleep or temporarily paralyze others. He was able to induce amnesia to a Lord Technologies's guard.
Psionic blasts: J'onn can project a powerful "Mental blast" than can hit the target mentally or leave them unconscious.
Psychic illusion: J'onn can project realistic illusions in other people's minds and make them experience things that not actually happen.
Psychic translation: As a Green Martian, J'onn can psychically translate other languages.
Telekinesis: J'onn can move and manipulate multiple objects with his mind. He can also generate telekinetic shield and shock-waves. J'onn was able to shove, grapple and pull Jemm without touching him and while being several feet away, as well as seemingly make a metal grate fall from the ceiling into Jemm's path to separate him from Alex several feet away.
Flight: J'onn can use the telekinesis to move himself, and simulate flight. When flying he is able to easily keep up with Supergirl, who can go over Mach 3.3 and keep up with the Flash (who was able to move at Mach 3.3 at the time) while teaching her proper flight tactics in battle, although he is notably slower than Superman, Supergirl and the Flash respectively at their top speeds.
Shock-waves: J'onn is able to project waves of telekinetic force to hit, propel, crush or cut a target.
Telekinetic-shields: J'onn is able to generate a shield of telekinetic force for different purposes (such as to block or deflect incoming attacks, or to contain a target).
