Jack's history is exactly the same as that of Earth-616's Jack of Hearts up until the Marvel NEW! relaunch.
Jack was always skeptical as to how he was revived by Jill, an ordinary human. It was not till much after his revival that he found out the truth. He was revived by a portion of his own power extracted from him during his sleep prior to his death. From this portion of his blood, they were able to duplicate the Zero Fluid injected into him by his father many years ago. The Zero Fluid was able to enhance his healing factor to the point of revival. Jack was satisfied this answer, but was confused as to why they took blood in the first place. It wasn't until he single handedly took out an entire army of Jack-Bots that he realized Project Pegasus made an army based off his powers. It was also because of this that he earned a place on the Avengers.
Jack of Hearts has all the same powers as he did prior to the Marvel NEW! event, amongst these powers are.
* Zero Energy Blasts
* Flight
* Superhuman Strength
* Superhuman Stamina
* Superhuman Durability
* Accelerated Healing Factor
* Scanalyzer Enchantment