First problem with Supernova: "As a standard action, deal fire damage to nearby foes who fail a Reflex save."
It does not impact only nearby foes, but rather all nearby creatures, making even allies subject to damage.
Additionally, Supernova and Black Hole do not have anything on the sheet designating them as Zenith Revelations (and therefore only usable when fully attuned, and you become unattuned after using them)
For context:
Solarian supernova states:
"When you’re fully photon-attuned, as a standard action, you can deal 1d6 fire damage plus 1d6 additional fire damage per solarian level to all creatures within 10 feet of you. A creature that succeeds at a Reflex save takes half damage. At 9th level, you can increase the radius to 15 feet, and at 17th level, you can increase the radius to 20 feet. After you use this revelation, you immediately become unattuned. Supernova functions as a zenith revelation for the purposes of abilities that reference them."