The following answer was only applicable prior to the EDIT adding the following text: "EDIT: i [sic] have just found out that EPP is trying to oust me and the other DM from our group while we're away at college, behind our backs. Needless to say, we're both pissed."
The section preceding the line break is in response to this development, but the remainder of the answer is for anyone in general who may be dealing with such a player.
It sounds to me like EPP has his frustrations and has gotten tired of dealing with them, just as you had gotten tired of dealing with the frustrations he has given you. I'm not going to jump and say EPP is a jerk, because his actions could have a variety of causes and it very well may just be that he thinks you, the DMs, are the issue and is trying to get you to leave for, in his mind, the betterment of the table. In a way, this is the same thing others suggested you do, just with the roles reversed. I'm not saying what he is doing is right; I don't believe it is. At the same time, I don't think you should get angry at him either. I get it, he's trying to oust you from the group, not just the table, but there could be other reasons for it that you don't realize. The best thing you can do is sit down with him and a third-party member of your group that you both can trust to represent both sides fairly in case you need a witness to explain what went down between you and EPP (or set up a camera); and, with this person/camera there, try to talk things through with EPP. Find the problem rotting your relationship away and either solve it or end things then and there. There's no need to throw away a relationship that can be fixed if you can avoid it; but, there's also no need to keep a bad relationship going that will only get worse.
I think I see the issue, and if you don't mind me saying, it does in part trace back to you allowing certain things beyond RAW. If this comes across sounding like an indictment of your ability as a DM, forgive me, that is not my intent. Anyhow, let me breakdown each part of your question.
Hey [Tuskiomi], I'm not gonna lie to you [EPP] is kind of ruining dnd for me Outside of sessions he keeps trying to prove me wrong with things,
This isn't necessarily a bad thing. Sometimes the players are right and know things that the DM doesn't and/or things the DM forgot. While I know this was your friend coming to you about EPP, I feel this may be something you both want to remember. There is an out, however: "What the DM says goes." It's the "Golden Rule" of RPGs for a reason. If you really don't want to deal with his shenanigans, simply tell him. "That's all well and good, but but you need to stop mini-DM-ing. If you take issue with how I run the game, think to yourself that it is a 'House Rule' and leave it at that."
And in session, he wants to prove his character is the main character
Is this necessarily a bad thing? If he's trying to do so in the Meta, just tell him "actions speak louder than words" and "if you think your character is the MC have them act like it." It can create some interesting character dynamics in-game and allows for a bit of a wild card factor, resulting in a, potentially, more entertaining time for everyone. Of course, if he persists in the Meta, tell him to knock it off or he'll be asked to leave. One of the core rules is "have fun and help everyone have fun." If a player refuses to try to let people have fun after being told to knock off a specific intrusive behaviour, then the group may be better off without that player, but give the player the chance to correct their attitude by addressing it with them one-on-one in private first.
EPP: I want to do two characters.
Me (Dm): Okay, but you're splitting XP between them
Result:The characters got killed early on due to his being behind the curve.
This is your call in the end, but personally, if a player came to me with that request: I'd either shut them down by saying that I, as a DM, don't think I can handle an excessive number of characters; would require the player to run them as basically one character just with two bodies, meaning their stats and skills are shared and they share a turn, but during out-of-combat, they can act independently; or just let them run the two characters. By imposing the "split XP" limitation, you doomed the character before the campaign began. If EPP is a new-ish player, he may not have understood what your limitation entailed.
EPP: I want to roll persuasion for (some rediculous thing that you couldn't convince someone)
Me (Dm): sigh okay roll.
Result: He actually rolls for it. Now automatically rolls to try the same thing. I have to stop him.
You shouldn't let him get away with these kind of rolls if the goal is supposed to be impossible. Just say, "Even if you Nat20'd, there's no way you'd be able to persuade {target} that {unreasonable roll request}. I can only allow things that are possible in-game. You wouldn't expect me to let a human Ranger roll Strength (Athletics) in order to fly, would you? This is equally impossible." If he pushes, tell him "DM rules it a 'No'. It's a good idea, but might I suggest coming up with something more believable?"
EPP: (combat) I'm going to do this action.
Me (Dm): Okay roll.
EPP: rolls. Okay now I want to do... (goes on for minutes, stalls combat)
Result: other players don't get the time in combat that he does. others get bored.
RAW is quite specific about this, during Combat, each turn you get 1 of each of the following (unless something specifies otherwise): Movement, Action, Bonus Action, Interaction, and Reaction (on others' turns). If they want to roll for something, such as Wisdom (Perception), tell them that it will count as their Action OR tell them what they can do for it to count as their Interaction. A Round is about 6 seconds. Unless their character is a genius with Super-Speed, doing more is generally not feasible. While I am obviously referring to D&D for this ruling, I am fairly certain this is standard across most, if not all, RPGs.
EPP: I'm rolling [stat] for [action].
Dm: No, you can't do that because [reason]
EPP: [rant]
Result: EPP rants and ruins the moment for everyone.
If he starts the rant, cut him off saying, "You have exactly 5 seconds to convince me or we'll continue the game with or without your cooperation," or "I am the DM and this is what I rule the situation as." If he's persisting past this point, ask him to leave. Again, it's important that the players have fun. While it is your job as DM to facilitate that, it's equally on the players to keep things "believable" in order for the actions they perform to feel meaningful.
Me (Dm): it seems like 2/6 players cannot make it, let's reschedule.
EPP: [rant]
result: EPP rants and now nobody wants to come to the next session.
Cut him off as he starts by saying, "I am sorry if this is inconvenient for you, I understand, but imagine how much more inconvenient it will be for the party if the leveling between you all is inconsistent." If he presses onward about it, you can either say, "We're going to reschedule," or "You can just stop coming if you have an issue with my decisions."
EPP: I want to (so something that's essentially two characters).
Dm: Okay
Result: EPP is massively overpowered.
That's on you for allowing him to do something resulting in him becoming overpowered, regardless of if you didn't realize the result or if you did but allowed it anyways. You're the DM. You don't have to allow everything they want. Sometimes, being the "bad guy" is necessary. Don't be afraid to tell EPP and others "no" and don't be afraid to ask them to leave if they are being regularly disruptive and unreasonable. EPP, as a player, has to take his lead from you, the DM. If you allow something he wants to do, that will set a precedent for the rest of that campaign, whether you mean it to or not. If you know he's trying to do something that can result in him being overpowered, tell him no or put a balancing factor on it. Otherwise, the result is your own fault. If he keeps pushing that it's his way or the highway, then tell him to hit the road.
EPP is really only there for the combat. This is not inherently bad, but to EPP, anything that's not combat is an issue. He's tried to fight PCs who were not provoking combat in anyway, and we've done a full party restrain on him before.
As long as it is within his character's alignment and described personality, I don't see the issue here. If a player is acting outside of what his character would naturally do, just follow up with, "Or {Character's Name} would do/say that if [he didn't know better]/[it wasn't outside his temperament]." He can't complain if you high-jack his character when he's trying to act in a way the character would never act. If it is something the character would do, then 1) let the character be taught a lesson by the others, 2) have your campaign's equivalence of "police" arrest him for assault forcing him to be stuck in prison for a set amount of time, (increasing the length of time up to and including the possibility of the death penalty based off of if his character resists arrest and/or kills any of the guards/knights/police/etc) or 3) punish him by giving the next encounter natural advantage on attacks against him or have it so that the next encounter is specifically going after him and see how likely the people he attacked are to jump in and save him. I know #3 is sort of a cheap solution, but sometimes players only learn that combat isn't everything when they are stuck in situations where they can't easily win from combat alone. Personally, I tend to do this by making every encounter capable of being resolved in three ways: combat, puzzle solving, and discussion (or some alternate form of appeasement in the event the creature is not capable of having a discussion such as if vs a pack of wolves).
This is a small number of the things that EPP does, and we've talked it over with him for every one of these issues, and some of them persist and some of them don't, but the fact of the matter is that every time that we have to talk to this player is a problem that all the PCs have experienced, and should have not happened in the first place, and puts a sour taste in their mouth.
Some of these things are perfectly reasonable on EPP's part and are more indicative of your inexperience as a DM in regards to players such as EPP. (This kind of inexperience is not a bad thing. I'd rather not have to deal with players like this when possible than to have regular experience with them, so don't look at this as a criticism of you.) That said, you say you have talked with him on each of these points before. That's good, but if it's an ongoing issue, talking alone is clearly not enough. He may not understand what the problem is with him doing these things, especially when you as the DM allow him to do so or when you don't stop his rants when he begins them. Think of D&D and other RPGs as game engines, not games. The game is what you are creating: the campaign. He's playing your game, not the other way around. Does he try to argue with GTA or Final Fantasy when something doesn't allow him to do something unreasonable? Probably not. He likely just accepts the game's limitations. This is no different. As long as you are firm with the rules, then he should either fall into line or quit showing up on his own. Give him an inch, though, and he'll keep taking the miles.
Should we ask EPP to walk? if not, what do we do to deal with this player who simply wants to be better than everyone else?
If you see no other way out, sure, ask him to walk, but the issue is also in part with what you, the DM, are allowing him to do and get away with both in-game and in the meta. Now, I don't know how he is acting with the DM of your current campaign, maybe it's the exact same, but it's possible that the cause of EPP acting out in your friend's campaign is the same: too much softness with the rules. Players like EPP can make for fun and enjoyable experiences, but you as the DM have to learn how to work around and with those types of players, and it takes time. At first, it'll be a lot of "You can't do this," "DM says no," and "You can leave if you don't like how I am running my game"s, but after you get used to figuring out how to outwit his machinations, it can potentially make the game more fun for everyone. Worst case scenario is endure this campaign and don't invite him to future campaigns.