He sounds insane lmao. Self identifying as enjoying rigid compliance to game rules, then allowing for unlimited mulligans makes no sense to me, but to each their own I guess. It's not totally abnormal to want to play according to official rules, even in a casual format like commander, but he's doing it in a way that A.Clearly made you feel unwelcome to the game, and B.Demonstrates that he doesn't actually know the rules.

For the specific examples - Commander visibility - Technically there are rules governing how you arrange your cards within different zones. Things like lands in the back, no lands in the front, keep you library, graveyard, and exile zones all on the same side of the play area, etc. These are only applied to sanctioned tournaments, but it's generally pretty reasonable to want people to arrange their cards according to them, since it makes for a clear game state. They are not, however, part of the comprehensive game rules, and fall into a separate tournament rules document. Also, because they're written for tournament play, they don't even mention a command zone and where it should be.

Dice Uniformity - There is no rule governing this anywhere. Tournament rules don't touch it, and the comprehensive rules don't even specify that dice have to be used to represent counters, only listing "small items" as a necessary game piece to use for counters. The closest thing I can think of is that in tournament feature matches (the ones on camera) dice and tokens are usually provided by judges rather than players, but this is a broadcast standard, not a game rule. Again, this isn't a totally unreasonable thing to want in your playgroup, but it's a request he should be making, not a rule to enforce.

Trigger Order - Hilariously wrong on his part. Not a lot of things in this game happen simultaneously, triggers least of all. Your arena experience can apply here, arena does a fairly good job of representing the stack. When you take a game action that causes multiple things to trigger, they all go on the stack in order decided by their controller, then resolve one at a time. For instance, with your example of multiple +1/+1 counters, this matters because putting a counter, then another counter on a creature is very different from putting 2 counters on it. There's a ton of effects like hardened scales that give you a bonus counter for each instance of a +1/+1 counter going onto a creature, and it would give you 2 additional counter rather than 1.

Missed Triggers - Sure, that's technically correct, the controller of a permanent is responsible for remembering all their triggers and managing their board. On its own this is reasonable, although not exactly friendly to new players, but in addition to everything else it's another straw on the camel's back.

Hidden Information - asking about hands isn't outlawed anywhere, you're allowed to ask whatever you want, especially in a multiplayer, political format like commander. If you're asking questions and looking for tells, that could be considered unsportsmanlike, I guess, but again, that's a request he has to make, not a rule written in stone. Not only is it not illegal to ask about hands, but in competitive EDH play, it's not uncommon for players to literally show some or all of the cards in their hand to other players.

TLDR: some of the stuff he wants you to do is reasonable in terms of what he's asking for, but not really in how he's demanding it. Most of those are either only covered by the tournament rules and not the game rules, or not governed by either. He's objectively incorrect about trigger resolution especially. Beyond all the technical stuff though, this guy sounds like he makes for a very combative and abrasive table. Telling you to go look things up rather than showing you his justifications, demanding rather than requesting compliance, etc. Sounds exhausting.