Consider his perspective for a little while.
Most player misbehavior comes from playing around.
A lot of your complaints come from the fact that your player is not taking the game seriously. He is not taking the game seriously. The game is a thing of humor for him. I repeated that for a reason: He's enjoying himself. That's what we tend to do when we play.
Now, with that in mind, let's address the misbehavior:
Clowning
Clowning around is one of the main things that I've encountered as far as issues go. Fortunately, it's not malicious, nor is it particularly damaging. I had a huge problem with this in my first campaign, where I was being all dark, grim, and serious as a novice cyberpunk GM and my players were exploring the effects of their actions on the poor, hapless denizens of the world they were turning into a mess.
This is when they do stuff like buy nine thousand llamas to crash the economy. They're doing it because they can, but they're not ruining your game. My foremost advice when this occurs is to just let it happen. Your player is enjoying himself, and the other players will likely remember it fondly. If you must clamp down on it, be sure to do so with the consensus of other players, instead of just trying to end the "misbehavior" that everyone but you is enjoying.
Redirecting
I've often had players just not be satisfied with the way my campaigns go (and I've been on the participating side of this as well) and decide to intentionally mess with my plot points to redirect the campaign. Ninety percent of the time this has occurred in my games it's been either the result of good in-character roleplaying (for instance, demanding the best gear if the character being played is a greedy, self-serving jerk), or the result of a total lack of interest in the current direction of the campaign.
To deal with redirection, sometimes a soft approach is better. Give your players what they want. Remember that roleplaying is collaborative storytelling, and even though you're doing the lion's share of the writing and creative process you're still responsible for listening to others' inputs when appropriate. Never assume malice when curiosity is just as likely the driving force; I've had players try to kill important NPC's just to see how I'd react, and while it's annoying it's also a way to prove yourself as a good GM by reacting prudently and without exploding (though specifics depend on you and your style).
Trolling
Sometimes players troll you. They'll lock all the other players' characters in a bomb shelter, but reinterpret the meanings of the phrase to result in a deliberate invocation of the "chunky salsa" rule and make everyone re-roll their characters following some explosive goodness. This is usually the result of a player who's bored, discontent, or offended in some way and wants to make the campaign more "fun", perhaps at the expense of everyone else.
The important things to look at when dealing with a troll are rehabilitation or removal. Sometimes it's enough just to ask them to stop, politely. Don't place a "red line", either. It's a great way to get a player to quit in a blaze of glory having killed everyone else's characters. Other times you need to just ask a player to leave temporarily or permanently because their behavior is just so disruptive, but this should be a last resort following other remediation (i.e. the one-on-one chat). Manage trolls privately, not in front of the rest of the group.
A closing note:
One thing you may need to do is set guidelines for your player. If they're constantly playing the same character's mindset, but just remaking them according to different rules, you may need to set boundaries and restrictions on them. Consider very carefully that your player sees things differently than you do; if he doesn't know where things are going, he may very well be disruptive without knowing it.
Also remember that he may be playing the villain in lieu of your NPCs; I've seen this happen multiple times in my group because one player or another doesn't think that the core conflict is interesting, and injects another one to the group dynamic just to liven things up.
If you don't read anything else, read this: Get in your player's head and talk to him before taking any action, communicate your concerns and expectations, and be prepared to use in-game consequences or removal from the group only as a last resort.
Your character can call things differently than your character sheet. If your sheet says "greatsword," but your character keeps referring to his zweihander, an AL DM would not have any grounds to stop you, as there are no rules for role playing (aside from alignment restrictions, rules of conduct, etc). You can play a halfling that insists, in character, that he's a hill giant, or calls his dagger a potato, so long as your character sheet is AL legal.
As for what is considered legal to put on your sheet, Jeremy Crawford tweeted in response to a very similar question on 9-May-2016:
The wuxia weapon names in the DMG (p. 41) are available to a member of any class, if the DM gives the OK. #DnD
So, only those weapon names listed in the DMG can be used on your sheet, and only with DM approval. Without it, only those listed in the equipment chapter should be on your sheet.
Source: https://mobile.twitter.com/JeremyECrawford/status/729786362010869760
Best Answer
You can run an AL game no matter what anyone else says.
From the Adventurers League website:
You, as described, are doing all these things and so are perfectly within your rights to use the AL trademark to describe your games.
When DMing in a store ...
Now the store may only be happy to host you if you participate in whatever they've set up, including their delegation of some authority to a store "coordinator." I'm not quite clear on whether that's happening: you say the employees don't know anything about AL, but you also say there's a store site where AL is posted and apparently the store "supports" some AL games. There may be more going on here that you aren't aware of?
Back to Adventurers League....
AL used to be, well, a League. There were site coordinators and regional coordinators and you had to sign up and have a password and whatnot. (I was a site coordinator for one site and a GM at another.) Circa season 4, with the launch of DMs Guild, all that went away. Adventurers League is, frankly, now a set of published play-conventions.
This is all to say that this "self-appointed organizer" has no business telling you what to do in order to bill your game as AL. But they may be used to being in the position of telling other AL DMs what to do, if they were a coordinator.
Solving your problem
You need to get the store involved, in my opinion. You are trying to run a game in the space they provide (presumably hewing to whatever rules the store has for that). Another store patron is harassing you. (Again: it may be the case that they're coming from a place of confusion or habit, not malice.)
There are "official" organizers of AL who these days mostly (to my understanding) work with conventions and the online community. You can find their contact info either at the website or on the AL facebook page (very active, that one), but I don't think that's the best way to go. Having been a site coordinator for years and then having that support disappear four years ago, I advise just working with your store.