When Green Lantern is rescued after revival in Season 3, he has his ring and therefore costume back. Unless Brainiac retrieved the ring and the body after Superman and Wonder Woman were fighting, this doesn't make any sense.
Braniac has shown he can teleport and therefore swap out large masses of land on the island, but he seems incapable of doing the same to LexCorp and the Hall of Justice. Though this may be due to Hack and Lex-2 having programs to deflect targeting said locations; leaving Brainiac to continued the war of attrition.
Brainiac tries using Superman and Flash's powers together and Green Lantern and Superman's powers together. But he does not try using Flash and Green Lantern's powers together.
The final battle does not count as Brainiac uses a power per body.
The final battle does not count as Brainiac uses a power per body.
After killing Green Lantern, King Shark puts on the ring and gains the Lantern's powers. This goes completely against the lore from the comics, as when a Green Lantern dies, the ring flies off on its own and seeks out a new wearer, not just anyone can put it on and gain its powers. Furthermore, the ring would never allow its wearer to use the powers for evil purposes, so if Green Lantern was being manipulated to perform evil, it would leave him and render him powerless.