I suspect that there is an underlying issue here which has little or nothing to do with the rules. He's not "lawyering" in the usual sense - probing the DM to see what loopholes he can exploit. What I gather from the description is that he's second-guessing the DM with regards to how difficult the encounter is.
Personally, I would do two things. First of all, I would have a discussion with your players about allowing DM creativity. For most of us DMs, a huge part of the fun of DMing is being able to create encounters, plots and schemes using this wonderful medium. When the players start second-guessing the DM over such details, it takes away from your fun. You had fun creating that encounter and hoped that it would be a source of fun for the players, too. The kvetching worked against that. Be clear on this: DM's should get to have fun.
Second, I would talk to that player about what was the real trigger there. Is it really that he views D&D as an entirely closed gaming system and any deviation from the canon is bad-wrong-fun? Was he worried about a potential TPK and thought that you were expressing a mean streak? Or perhaps he's a frustrated DM himself and can't help but put himself "behind the DM screen"? He might not know himself, but hopefully you can tease that bit of information out of him. If it's the first item, then continue that discussion about creativity. If it's the second, then he'll probably get over it after you play for a while and he gets used to your style. If it's the third, you might find ways to involve him in your DMing - perhaps he can design your next big boss encounter for you, or you can busy him by arranging for the party to obtain a stronghold which he needs to populate with guards and traps.
TL;DR: Talk it out. Express why this incident bothered you, establish the parameters for your own fun, find out what bothered him, and take his concerns into account in future games.
(This is advice for games that are played in person or in a largely synchronous setting like a chat. If you're playing by forum a lot of it won't work well just from your end, and you'll need to establish an alternate gameflow by sharing your players' concerns with each other up front.)
The hot-headed fight-happy freebooter who has to be restrained by the better angels among their companions is a reasonable character to want to play, and you can make it work, but not accidentally. It's possible for characters in Dungeon World to meaningfully clash with each other without running into the issues that might arise in a game with a more rigid action structure.
I'll say this up front: it's only going to work if both sides are okay with letting the dice settle this, and that means being okay with every possible outcome, as long as they get their chance. If Leafwillow and Sir Justice's players are cool with trying and failing to hold Grognak back sometimes, and Grognak's player is cool with trying and failing to get out from under Leafwillow (who is currently a hippopotamus with a wooden leg) sometimes, then everything's cool.
So here's how to make that happen. Well, first:
0) Nothing Happens Unless You Let It
Dungeon World is a conversation. When you're having a conversation about where to get dinner and somebody shouts "Jack in the Box!" you don't all just immediately go to Jack in the Box because it's the first thing somebody said, do you? You let everyone talk about where they want to go and make a decision together after hearing what everybody has to say.
In much the same way, when you're describing a tavern scene and mention a cloaked figure, and Grognak's player screams "GROGNAK SMASH!" and pitches some dice, that doesn't actually mean that Leafwillow and Sir Justice have to stand there poleaxed while Grognak smashes through three poker games and a marriage proposal to get at the cloaked figure. You're the GM. You control the universe. Nothing is going to happen until you say it does, and that means that you can take Grognak's input without saying what comes of it, and then turn to Leafwillow and Sir Justice and let them have their say.
Okay, they've all had a chance to tell you what they're doing in this open-ended scene. Now what?
1) How To Stop A Fight
Dungeon World has no concept of initiative order or equal goes. People take actions and get the opportunity to take actions as it is dramatically appropriate.
So, when Sir Justice stands in defense of the tavern patrons and rolls Defend, and when Leafwillow frantically grabs at Grognak to hold him back and rolls Interfere, this doesn't "use up their actions". It's not "Grognak's turn" again. You get to decide how the tavern reacts and who gets the spotlight as a result of it. "I'm going to let go" could turn out to be excellent leverage for Leafwillow to Parley with the cloaked figure, for example.
This second bit is the more usual flow of running Dungeon World, by the way. Everyone entangled in a dramatic situation, and you pick one person at a time to talk to and make some progress on their corner of it. For those times when you're just describing the world and not necessarily looking at anyone for an answer, you're not obligated to humor the first person to speak up - you weren't talking to anybody, so you can wait to hear from everybody.
2) A Little More Conversation
But you also mentioned wanting their characters to talk to each other more, which is also cool. So here are some ideas for letting that come out.
- You can put a decent amount of "dead time" in Dungeon World, after you stop running down the collapsing building of the first session. There are Perilous Journeys to Undertake that last days at a time, Making Camp means there's a watch to set as people settle in for the night, and sometimes you need to wait until it's dark out, or bright out, or the dragon gets bored with inspecting every hidey-hole in the mountainside and flies away. In those times you can prompt for some reflection and conversation. Not, like, full-on community theater conversation, if that ain't everyone's jam. What do you talk about? Well:
- Everyone's written bonds with each other, right? Grognak's put Leafwillow and/or Sir Justice in some of his bonds, Leafwillow and Sir Justice have put Grognak in some of theirs, and everyone's been okay with where they wound up? Everyone has to be okay, by the way. That's a rule. You can't write down a bond that one side isn't good with being a part of. They might not agree with what the bond says, but that's just what the character holding the bond thinks. Ask both people involved in the bond how they think it might resolve. Maybe a conversation's a good way to make that happen.
- Heck, nothing says Leafwillow has to actually try and grapple with Grognak to roll Interfere. A stern talking-to can be just as distracting.
If people are okay with playing off each other dramatically, okay with not succeeding at their violence/nonviolence as long as they've had their go, then having some of your adventuring group butt heads now and again can make for some really satisfying drama. Just be ready and willing for either side to come out on top.
The first thing you need to do is figure out whether this problem needs to be resolved in-character or out-of-character. Is the warrior's player doing this because the player enjoys this kind of PvP activity? Or is he doing it because he thinks it's what his character would do?
If it's the latter, then you should take a look at My Guy Syndrome, then use the answers there to help you discuss the issue with the player. If it's the former, then you need to sit down with the player, away from the game, and ask him why he's so invested in attacking you. Explain that this isn't fun for you, and that you want to work with him to find a way to support his character's backstory without having to spend all your time unconscious and not participating in the game.
For example, in my current game, my character and another character don't get along (though the player and I are good friends). My character frequently "attacks" the other character, but those events are strictly roleplay - no dice are rolled and there's no in-game effect, just a fun interaction. Another possibility would be to have a third character get involved, someone the warrior respects. This third character could say to the warrior, "I know you hate mages, but we need the warlock to accomplish our goal. If you keep knocking them out in combat, you're putting the rest of us at risk." Roleplay solutions like these help the player feel like their backstory and RP choices are being respected, without negatively affecting other players' characters.
A few key points to keep in mind when having that discussion: RPGs are supposed to be fun for everyone involved, and the whole group is responsible for maintaining that fun. If this player's actions are preventing you from having fun, that's not fair to you (and potentially the other players, as one frustrated and upset player can often bring down the whole group's mood, however unintentionally).
Depending on the player's reaction to this discussion, you may need to get your DM involved. Talk to your DM privately (not with the warrior's player present, to avoid anyone getting ganged up on), and explain the situation and why it's frustrating to you. Ask the DM if they can do anything to mitigate the issue - perhaps to enforce these attacks as roleplay-only, or to help give a story reason for the warrior to stop attacking you.
TL;DR: Make sure My Guy Syndrome isn't the issue, then work with the player to find alternate ways to RP their character that don't negatively affect you.