I know that after 1000 meters there is no light under the sea. Could Percy Jackson see in the dark, if he was under the water?
Yes, he has some limited underwater vision.
This is made clear by a quote in The Last Olympian:
Beyond this, the sea floor stretched into gloom. I could see battles raging—flashes of energy, explosions, the glint of armies clashing. A regular human would've found it too dark to see. Heck, a regular human would've been crushed by the pressure and frozen by the cold. Even my heat-sensitive eyes couldn't make out exactly what was going on.
Percy Jackson and the Olympians, book 5: The Last Olympian, chapter 2: "I Meet Some Fishy Relatives" (emphasis added)
So while he can't see perfectly underwater, he does have some limited special vision.
Not only can Percy see better underwater than regular mortals, but he can also sense the presence of many things when they are underwater, as though he has the ability to use sonar.
I should've been blind, too, this deep in the water at night, but I could see the heat from living forms, and the cold of the currents. It's hard to describe. It wasn't like regular seeing, but I could tell where everything was. Percy Jackson and the Titan's Curse -- Chapter 8: I Make a Dangerous Promise