Ambiguously Brown: People are shown a little bit confused over the fact he's got slanted eyes with a nut-brown complexion. He identifies himself as Filipino, but his origins become more dubious after the Slaughterhouse Arc.
Badass Bookworm: He writes essays as a hobby. Wally is horrified when he learns it.
Bad Powers, Good People: He can cut anything and manipulate anyone, the perfect recipe for a killer, yet Edge strives to be a hero.
Faking Amnesia: His cover story when he has to explain his circumstances to the League. It could be a subversion.
Fish out of Water: Downplayed but there is minor differences in the Justiceverse's lifestyle compared to what he knew in his home dimension. Played for Laughs when he asks for Coke, which Artemis misinterprets as him wanting to do drugs.
Foil: Just like Taylor Hebert, he's saddled with a very morally-iffy superpower, can be extremely pragmatic and desperately strives to be a true hero while constantly berating himself. Bonus point for meeting a genuine hero right after stopping a villain and making a deal with him.
From Nobody to Nightmare: As Batman explained it to the League, Edge has the potential to become a truly successful assassin - he has the cunning and skills for it.
Good Is Not Soft: He shreds a werewolf to ribbons to protect Dr Roquette on his first mission and only stops Artemis when she tries to kill her father because they are in public and need to maintain a good PR, later promising he would help her hide the body.
The Heart: Since his power allows him to manipulate anyone, he uses it to create and reinforce the bonds between his teammates.
Heroic Self-Deprecation: He may not be a psychopath but he still refuses to consider himself a good person and hopes the League's genuine heroism will end up influencing him.
In the Blood: His biggest fear, which would lead him to become Jack Slash Mk 2.
Informed Judaism: He told the Kaddish for a funeral but is otherwise a self-professed atheist.
Knife Nut: But of course. His main weapons are a kukrit and a karambit.
Mundane Utility: Exercising his cutting power in the kitchen certainly is this.
Nay-Theist: Yes, he's now stuck in a dimension full of aliens and magic entities and genuine deities. He's still an atheist.
Berserk Button: She outright blows her top at Wally when the speedster declares Edge cannot be trusted because of his supervillain father. It hit quite uncomfortably close to home, after all.
Defrosting Ice Queen: She starts antagonistic towards Edge, thinking he's constantly mocking her and wanting to put him in his place. Comes the Slaughterhouse arc and her entire position towards him does a full 180.
Good Is Not Nice: Very much abrasive and has no problems about killing a criminal, even if he's her father. Especially if he's her father.
Not So Different: From Edge. She too struggles with the fact she's related to a villain and desesperately wants to rise above daddy's reputation and be a true hero.
Stunned Silence: Her reaction when Wally blurts the team thinks she's actually Green Arrow's daughter.
You Are Better Than You Think You Are: Basically the effect when Kid Flash confesses the Team's theory about Green Arrow being her dad - if they can believe she's related to a hero then she has to have some heroic qualities.
You Are Not Alone: Every negative thought Edge has about being a monster's offspring, she already had, and as such is well placed to support him when he crumbles.
Miss Martian a.k.a. M'gann
Child of Two Worlds: She really wants to fit in Terran culture but she can't help drawing comparisons with Mars.
Cuteness Proximity: Edge's psychic babble reminds her of a toddler trying to broadcast their first words. Edge feels a bit emasculated when she gushes over how adorable it is.
Fantastic Racism: The sorcerer-priests from Mars preached White Martians were inherently wrong due to incomplete souls. She assures Aqualad and Edge it's okay because they don't preach anymore and she's Green but she's quite uneasy and stiff when talking about it.
Be Careful What You Wish For: He wanted to become the second Batman. In the Slaughterhouse Nine Arc, losing his adoptive father throws him on the path to revenge, just like Bruce Wayne was driven to vigilantism by his parents' murder.
Break the Cutie: Brutally shaken by the Slaughterhouse Nine event, he tearfully admits to Batman it changed his outlook upon superheroism. And learning about Earth Bet doesn't help.
The Gadfly: He ought to be called the Troll Wonder, seriously.
Sheltered Aristocrat: Not only he was adopted by a billionaire, he's quite naive about how dirty heroics can be, which means he's very much shocked and disgusted by Edge's decisions as a leader in the Slaughterhouse Arc and Earth Bet's general condition.
Trauma Conga Line: Not only Batman was killed by the Slaughterhouse Nine in the relevant arc, Alfred also was attacked and left to die - losing his family again led him to briefly adopt the "Crimson Avenger" persona.
Wide-Eyed Idealist: Starts with shades of this, but circumstances force him to drop most of it.
Superboy a.k.a. Connor a.k.a. Kon-El
Because You Were Nice to Me: He really starts to defrost towards Edge when the other boy calls him "Connor" while undercover - it was for the mission's sake, but it was the first time someone called Superboy by a human name.
Big Brother Mentor: Decides to assume this role after learning that Lt Marvel is actually a disabled kid.
Clones Are People, Too: Very much angsts about his condition, and his "father" Superman being quite deadbeat in the parenting department doesn't help.
Mind over Matter: His tactile telekinesis. He can broadcast his strength and will upon his surroundings, and this since after almost seeing a depowered Lt Marvel drowning in front of him.
My God, What Have I Done?: He was very hostile and envious towards Lieutenant Marvel for being a good-looking, Flying BrickNice Guy apparently interested in M'gann. He feels like crap when Freddy is de-transformed in front of him, revealing himself as a wheelchair-bound elementary school student. This plus the kid being about to drown leads Superboy to trigger.
Ship Tease: With M'gann, something their teammates are extremely enthusiastic about. They later make it official.
Loose Lips: Blurts out in front of Artemis that the Team knows Green Arrow isn't her uncle, right after being asked to keep mum about it. A chance for him that he explained and excused himself before being strangled.
The Nicknamer: Oh, yes. Calling his teammates Megalicious and Edgelord is the least of this.
Sins of Our Fathers: Bluntly declares Edge is untrustworthy because he didn't confess his dad was a murderhobo.
Ambiguously Brown: He's Black. Not African, not Polynesian, not mixed-blood, just Black. Atlantean is another thing entirely.
Older Alter Ego: Downplayed; his superpowered form is teenaged, but Freddy himself is only an elementary school student.
Foil: Compare with Armsmaster, who also uses lots of cool gadgets to fight crime, is very experienced in heroism and extremely no-nonsense, and was responsible for dragging a superpowered youth on the cape scene right after witnessing them taking a villain down. However, Batman is a lot much nicer and successful in keeping his impromptu ward on the right path.
Parental Substitute: Very much for Robin. There's also hints of this with Edge, as he manages to make the youth feel like a little boy again when grounding him.
Pragmatic Hero: His reasons for recruiting Edge are two-fold. First of all, Edge will not be deterred from the heroic path, and inducing him in the young team reduces the odds of him dying in a back alley without support. Second, Batman can watch a potential asset and ensure he won't be a foe in the future.
Reasonable Authority Figure: First points Edge could try to become anything other than a superhero, but accepts to train the kid after seeing he's not going to stop chasing after his dream.
Sins of Our Fathers: Does not believe in it. After the Slaughterhouse arc, he decides to consider Edge as his own man, not as Jack Slash's offspring.
So Proud of You: When a sobbing Robin confesses he doesn't want to become a second Batman, his mentor tells him such a decision makes him very happy. Because Robin shouldn't try to be Batman Lite, he should try to be Robin.
Terror Hero: Their first meeting ends with Edge fainting. The second is not much better.
Everyone Has Standards: In spite of his longing for a host, he's downright uneasy with Edge's second merging with him since the youth asks him to wipe his conciousness from existence and keep his body forever.