You've got a deep understanding for character development and you've been able to predict my original story almost perfectly.
So, here's the challenges that I'm facing, and maybe you can help me with these:
1. Due to the similarities in powers and the fact that Dissonance was thought up first, Vega has to lose to her. Almost always.
2. Vega Learns new abilities by trying to overcome disadvantages when fighting Dissonance.

3. Dissonance (unfortunately) got her powers 3 years after Vega in our universe, which throws out a simple time jump. Thus Vega comes from a universe where they both got their abilities at the same time and their stories unfold similar to what you said.

BRIEF Bio: Jen led a quiet life for her first 18 years. When she left school, instead of attending university, she joined up with the armed forces, determined to do good in the world. After a year of service, she was assigned to a special operations division, the SAS. She carried out missions for several years, seeing things that would make normal people break down and go insane. This led to her becoming withdrawn, often appearing emotionless to deal with what she had seen. After a particularly brutal mission, Jen refused the orders of her commanding officer when ordered to gun down some civilians. When threatened at gunpoint, Jen's powers awoke. She killed the rest of her squadron with them, partly due to their out of control nature, and partly because she wanted to. After that, she went on the run, dying her hair to help obscure her identity. She moved to New Athens, determined to change the world to a vision she wanted, one free from the governments and corruption she viewed as responsible for the atrocities she had to commit. There is nothing she won't do to see this happen.

4. I cannot time jump without pulling everyone into the future, therefore I can only jump from the past.

5. If this is an alternate universe, what happened to the original Adrian Hunter? (I'm thinking that he's dead too, like his mother) but Vega believes that the grave is an empty tomb made due to his disappearance, when in reality, it's not empty.

6. If this is an alternate universe, Vega believes that is is only a time jump for now.

7. Due to the time jump (New universe or not) Vega believes that this timeline is "false" and that all (or most) of these events happened because he was absent in the time jump. He develops an unhealthy detachment for life because he believes that he's simply going to go back in time and "correct" any grievances that happened as a result of accidental or intentional misgivings.

8. This detachment from reality (and possibly humanity) sometimes causes people to perceive him as a villain even though he's not and still believes himself to be the hero of the past (That people either don't remember because this is a new universe or that people scorn for abandoning them if it's the same universe).
9. Vega still believes himself to be good and so he won't compromise his morals even in a "false" timeline however, it's hard to care about something (or someone) that may never happen in his "true" timeline (His outlook on his current life).

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1/2. Of course, that's a given from what I can gleam on your CS. You'll have to discuss this between the two of you but what I would do is during the first fight Vega has his ass handed to him by Dissonance. She's had the last 3 years to use and develop her powers whereas your character had a short amount of time to develop his own before being transported by the black hole. The second fight would take place after some time and you've developed your powers against other characters, in this fight Dissonance would still win but you would develop your ability more and be able to deliver stronger punches and kicks like you state in your CS. More time will pass and you'll develop your character further and be able to punch and kick as hard as Dissonance's own punches and kicks with her ability. During your 3rd fight with Dissonance is where I would develop you gravity pull ability, but not realizing that the ability works in a sphere around you, you mistakenly pull in rubble from the fight knocks you unconscious. After this fight you develop that power more learning the range of the sphere around you and learning to focus it. The 4th fight you use all of your abilities that you have been developing and this fight ends in more of a draw for the two of you than an outright loss for you. All future battle between the two of you I would talk about and determine who would win or if they would end in more draws.

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3. Dissonance didn't get her powers three years after your character, she got her powers 3 years ago meaning she got them at around 22 year old while still a member of SAS.

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That's why I recommended just a time jump. You received your powers at 17/18 and went missing shortly after. While at the same time Dissonance's character was completely normal until at about 22 when her powers manifested, that makes her receiving her powers 4/5 years after your character received his.

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4. I'm not quite sure what you mean here.

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5. You keep talking alternate universes and I'm trying my best to find a compromise to keep us away from that because I think it would just be a lot of work on everyone's part. Because let's say that in our universe (The current one where the RP is taking place) Adrian Hunter found the meteorite that gave you your powers but in our universe it killed him. In your alternate universe your character and Carlsberg's went to school together and gained powers around the same time, that create a whole new history for an already established character that Carlsberg may or may not want to create. For instance, my character Reaper is a former member of STRIKE that faked his death and became a mercenary. In your universe he could very well still be a member of STRIKE. This is why I keep pushing the time jump, so we don't have to make secondary histories for characters in a universe that only your character is aware of.

If we do the time jump for the most part his grave would probably just be an empty plot with a grave marker or a coffin filled with mementos that others placed in the coffin.

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6. What I would maybe do is instead have him believe that it's an alternate universe, when in actuality it's only a time jump. That way he believes he can return to his own universe to save his mother from dying. This could also lead to how he treats others and until he learns that this is his universe and he was simply flung forward in time by six years he would then just try to find ways back in time while adjusting to the time he was found himself in, maybe trying to become a more civilian friendly hero coming to the realization that these people have their own lives that actions affect.

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7. Personally, I would stick with this idea as it's pretty much what every time traveler goes through.

"I missed the last 6 years of my life, and while the world continued moving I wasn't there to make any changes. What if I had been around? Would my mother still be alive? Would I be a better known hero? Blah, blah, blah."

Unless a better idea comes around this is basically every storyline any time traveler goes through. Take a look at DC's Flashpoint. Flash runs back in time and saves his mother, but the outcome of that changes the world that he knew. Friends become enemies, enemies are allies. So on and so forth.

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8/9. I would have him just come off as cold when dealing with civilians. He wouldn't do news interview or anything like that and he would just kinda push people out of his way so he can continue on with his mission. Like, let's say he's chasing my character down on foot and Reaper takes a hostage. I would imagine your character would just keep coming at me as if I didn't have a civilian at gunpoint. For the most part concerning your hero's identity from the past I would have it that he was just not a well known hero. Consider this, if in Spider-man's early days (when he didn't have his suit and ran around in a hoodie) he suddenly went missing no one would really have noticed. If he then reappeared after 6 years unless your hero was a well known hero no one would connect the dots that you and the hero from the past are the same.

As for what you posted in the spoiler in one of your latest posts. Reading it, while it's mostly just highlights, pushes into the God-mode territory which is a major no-no. If you went with something like that I would instead recommend that you can Carlsberg get together and exchange PMs or go into the titanpad to create a collaboration that way Carlsberg can control her own character and preform reactions appropriate for her.

@The Kid Lantern I may not be online but I'll be around. Just text me if you need me for something.