[RPG] Player is constantly drawing and scribbling at the table

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.

Well, there's no silver bullet solution. This isn't really an RPG problem, it's a pure-play interpersonal/psychological issue, variously called 'spotlight hog,' 'attention whore,' 'attention seeker,' et al. I'll call it "attention seeking," the more canonical term, going forward. In general especially for adults, "telling them to quit it and booting them if they don't" is largely the solution, which you did, but it does have side effects. What you - and importantly, the rest of the players - can do is to in general promote good behavior at the table (they can't leave it to you). Then, the solutions tend to be found in general work/parenting/etc. social discussions, like:

This article on mitigating attention-seeking behavior is targeted at small children, but frankly it's about as good as with adults, as this is at its core a "you didn't listen to the lessons about taking turns in kindergarten" problem.

A lot of the other articles on this tend to be fairly negative about the possibility of addressing this successfully in a group. This Psychology Today article closely links it with causing drama and pretty much says "yeah, that's hardwired." Even articles like this one about problem personalities at work say "just avoid them, don't try to confront/fix" because of how easily it just spirals into drama.

What it all boils down to is that all you can do is:

1. Give them positive attention when it is their turn
2. Set clear boundaries about not disrupting when it's not their turn; mention these expectations to the group
3. Don't let yourself be dragged into drama if they escalate to that when getting thwarted with their attention-seeking
4. It's not just the GM's responsibility, but the responsibility of everyone, to bring social pressure to bear on violating those boundaries. The Geek Social Fallacies tend to make many gamers not want to hold up their end of maintaining the social contract and push it off to the GM - that makes this as much their fault as the bad actor. Like we do on RPG.SE, remind everyone that it's mainly their role to keep things on track
5. Don't let this drag on - one bad session won't ruin your campaign, but if you let it fester for months it will. Move decisively to correct or cut out truly toxic behaviors y'all can't live with

I've dealt with attention seekers in both games and real life, and sadly that's all you can do and it'll only work about 50% of the time, the rest of the time you have to deal with it (work, family) or cut them off (friends, gaming).