Allen, Allen, Allen...

Where to start?

[b]1).[/b] Multiverse, but I'll explain why in response to [b]2[/b].

[b]2).[/b] Sandbox, to me, is one gigantic no no. As you said, they are [i]very[/i] hard to keep alive, and generally they just end up being a shitposting wreck because nobody has any actual objective: It'll be a good 10-15 pages of random ass interaction then [i]boom, dead.[/i] As for the superhero group idea, it works; It could loosely be based off the Nicktoons Unite games, where we have multiple big-time villains teaming up (Specifically ones from the universes characters chosen by the playerbase are from) to make one extremely nasty plot to take over everything. They start wrecking havoc in the multiple universes, and then... Well, we'd need a way to unite the characters to stop them. If I had to suggest anything, I'd say have Dexter build a machine to get them all to one place. Though where exactly this machine is built and how much Dexter knows about their situation would require a bit of thinking; Though it'd be obvious that Mandark would be involved on the villainous side as (probably) one of the lesser threats.

Also the plot idea above is cliche and generic, but it's just an example for the most part. (Unless you want to say 'fuck it' and roll with it after ironing some shit out, because it'd have plenty of interaction and action, which is mostly what I think most of us will want from this anyways)

We do need a plot. Without one, we're just making something that is almost certain to be short and bitter.

[b]3).[/b] [i]No.[/i]

[b]4).[/b] I think we should compile a list as a group, as there's plenty of shows out there. Right now we have from your post:
[b]Dexter
Powerpuff Girls
Samurai Jack
Generator Rex
Code Name Kids Next Door
Ben 10
Code Lyoko
Steven Universe
Sym-Biotic Titan
Xiaolin Showdown
Totally Spies
Ed Edd & Eddy[/b]
And, From Me:
[b]Foster's Home For Imaginary Friends
Camp Lazlo
Chowder
Courage The Cowardly Dog
The Grim Adventures of Billy and Mandy
The Marvelous Misadventures of Flapjack
Megas XLR[/b]

For the moment, I can't think of anything else to add to this list, so it's something to go on. If somebody wants to add a character from another universe we haven't thought to discuss or add down the road, they can feel free to ask if it's considered okay. 

[b]5).[/b] The Ed Boys are an interesting one. They can't do much directly (Aside from Ed, obviously) But that's their thing; Eddy is a schemer, Edd is the man that makes them work, and Ed is the necessary muscle for any group ever. Eddy and Edd would have to be a bit more indirect, but comedic value and good writing can be appreciated over enemies giving them a hard time, right? The way I see it, characters should interact with enemies in battle based on what they are. If they actually fight, Like Jack, Ben, or Oni does, then it'll seem more dangerous and actually threatening. If comedic characters like the Eds, Johnny, or Blu fight, then they basically become comedy skits. For badder enemies, like villains, this won't be able to fly, obviously; Perhaps make a forth-wall breaking joke like a "gag character immunity device" created by Mandark, or some shit. 

[b]6).[/b] I'd like to ask some basic things; Starting off with if we have a limit on the amount of characters we can use, or if it's based on what we can handle. I'd prefer to have everyone keep to one character if our group ends up big, but if not, doubling would be okay with me. Too many characters could get chaotic if we don't have anything to do with them. But, if you have a plan, then by all means, allow as many as you want.