Star-Lord's powers and abilities
Hybrid Physiology
Due to his heritage, he is part Celestial and part human, giving him superhuman abilities. Even while not having awakened his celestial power, Quill had enough power to briefly survive holding the Power Stone on his own and after awakening his full power, was able to challenge his father, a true Celestial, who had easily subdued the other Guardians. Although he seems to have lost his cosmic powers after Ego died, Quill retained his superhuman physical powers.
Superhuman Durability
Due to his paternal heritage from Ego, Quill holds considerable amounts of supernatural durability and endurance to the point that he even was able to physically withstand the exposure to the energy from an Infinity Stone. He held the Power Stone for a short length of time without dying, and was able to harness its power when sharing the burden with the other Guardians. Quill himself also noted that he was able to survive numerous injuries while working for the Ravagers, though none were implausible enough to raise any suspicion. When he fought Ego, he was able to withstand Ego's attacks and only had minor injuries at the end of the fight. Later, Quill managed to survive a shockwave from Thanos using the Infinity Gauntlet and quickly recovered.
Molecular Manipulation
While battling Ego, Yondu Udonta's encouragement allowed Star-Lord to realize his ability to manipulate matter. He used it to propel himself into the air at a high velocity. He was able to construct things and weapons out of matter, such as gloves of rock to punch his father and later he enveloped himself into a giant Pac-Man to counter the giant materialized by his father.
Energy Manipulation
While on Ego's planet, Ego taught him how to manipulate energy and how to use it to create solid constructions by drawing energy from the planet. He once created a ball to play catch with his father, like he always dreamed of. He can even empower his fists with energy to produce superhuman physical strikes, such as when he did with his father moments prior to his father's death.
Self-Augmentation
He used his cosmic power to enhance his physical strength and durability to the point where he was almost immune to damage, allowing him to easily smash through stone and survive crashing into the ground at bullet-like speed.
Immortality
While battling his father Ego, Ego told him that as long as Ego's essence is still alive, Star-Lord himself will never die.
Abilities:
Expert Combatant
Quill is considerably skilled in close-quarters combat, both in armed and hand-to-hand combat. He was able to stand his ground against Gamora, the finest assassin trained by Thanos, in a fist fight. He uses his two blasters as melee weapons to strike and knock his foes unconscious with a hard strike to the head with great skill. He was able to easily take down multiple Nova Corps, Kyln, and Sakaaran soldiers by striking them with the blasters. Quill also managed to easily subdue and hold the superhuman, but inexperienced Spider-Man at gunpoint during their brief skirmish, as well as dodge blasts sent at him by Thanos using the Power Stone and even plant an explosion on Thanos himself, although he did had aid from Doctor Strange's use of Eldritch Magic to conjure platforms, which helped him maneuver through Thanos' attacks and plant the device.
Expert Leader
Quill is a very capable leader, having successfully led the Guardians of the Galaxy ever since the group was founded. Still, he sometimes had a hard time keeping his fellow Guardians in line, like when Rocket Raccoon pretended to Thor that he was the captain of the Benatar and left with the God of Thunder to Nidavellir, or when he could not talk Drax the Destroyer out of attacking Thanos on Knowhere.
Expert Tactician
Quill is an exceptional tactician, as shown when after finding Iron Man's plan to suck, Quill took the lead and made his own plan to stop Thanos and was nearly successful until he broke the group�??s hold on him after going into rage on learning Gamora�??s death.
Expert Thief
Raised by the Ravagers, Quill mastered the art of thievery and evasion. Though Star-Lord had a criminal record, thievery was not one of the charges, though Rhomann Dey picked him up for petty theft.
Expert Marksman
Quill is well-versed in the use of weapons from all over the galaxy, but he prefers using his own Quad Blasters, which he is shown to be skilled with. He also handled a Kyln Guard's rifle, a weapon he was not believed to have even seen before, and easily shot and destroyed a drone with it. He even accurately shot Spider-Man during their skirmish and trapped him long enough to hold him at gunpoint.
Acrobat
Quill is highly athletic and has high level dexterity, reflexes, and coordination, which notably allows him to do parkour and freerunning. His extreme reflexes allowed him to effortlessly catch a small lunging creature trying to bite him while he was wearing headphones and seemingly distracted by his music. He was able to leap several feet across a chasm, perform a combat roll while sliding along his ship directly into the cockpit.
Expert Pilot
Quill is an accomplished starship pilot. He has used this skill to escape Korath and his men on Morag.
Bilingualism
While Quill speaks English, he is capable of understanding the Groot language after having spent four years with Groot.