Okay... there's a lot to unpack here. Some of it might be relevant to the DM being poor and some just a mismatch between player style and DM style.
He had said he had DM'd before, but I later learned it was for FATE Core, not 5e, and I think it was only once. He also said he had trouble keeping his group together because of player disinterest.
A good DM can get their start in any edition of game. Cutting your teeth and running FATE is fine and can lead to a good D&D campaign, albeit one with a potentially more story focused feel. Being a DM is as much about the story, presenting the setting, and managing the players.
I was also initially a little surprised when he said he didn't have a copy of the PHB or DMG. He said it was because "they change the rules so much it's pointless to buy anything", but I also got the impression that he was just completely broke and couldn't afford them.
How old is the DM?
This sounds much more like a older edition weary DM complaint. One who has seen the books come and go two or three times.
Once we started playing, it was clear this guy hadn't read much of the PHB at all, and I learned later that he outright refuses to read the DMG (saying it just has stuff about the planes, how useless), and even scoffs at the idea that anyone would run one of the WotC published campaigns.
As others have mentioned, the DMG is basically a big book of optional rules. While there are a few pages on running the game and being a good DM, it sounds like this DM might need
Robin's Laws of Good Game Mastering more. Or
Geek & Sundry's Game Master Tips. As the later is a video series it might be an easier sell (and segues nicely to your DM as they have seen Critical Role. You can pitch it as a way to be more like Matt Mercer since he is the initial host).
Do you need to read the PHB and know the rules? Not really. It helps to know the basics of the game, but if the players know their own powers that's fine. And if one person at the table knows the rules well enough to adjudicate, that's okay too, freeing the DM to manage the story and everything else.
He used some D&D wiki when helping create some of players' characters, but he didn't even realize the content wasn't even for 5e
That's a big red exclamation mark. D&D Wiki is basically a giant pit people who only half know the rules and content just shotgun ideas into.
(In fairness, 3e and 5e can be close enough in presentation that you could mistake them. Much like 1e and 2e. Although in terms of actual design they're kilometres apart.)
For about the first 3 months, we practically never rolled dice and very rarely fought things. Want to do something? "Yes, you do that" or "no, you can't".
*shrug*
That's neither good nor bad. That's just the story he was telling. You don't
need to roll dice for everything, especially of the DC is low enough that it's something your character should succeed at.
How often and long do you play? Was that three short sessions or 10 long ones?
One NPC we fought, a boss-type of character, was literally invulnerable -- we'd whack him and he'd just take it with no damage, not speaking or anything. Other fights we've been in were so ridiculously stacked against us, we'd spend 2 or more hours fighting a fight that we knew we were going to lose, or we'd aggro some characters that had AC so high we couldn't hit them at level 2 or so, but if we ran away they would just reset like some kind of MMORPG AI. One NPC he designed to ambush and kidnap us with special abilities that made him seem like god, but with faerie fire, magic missile, and 5 PCs chasing after him, even his god-mode NPC went down relatively easily (I think he just had no idea how to design combat).
This, however, is a bad sign.
He designed an island as a sandbox kind of environment with maybe like 5 or so locations in it that we can all get to in about a day's travel or less. The island is mostly desolate, so there's not even a lot going on. The one town is tiny with a store and no plot elements there. We occasionally fight random encounters that he comes up with, but they are frankly just a waste of time -- they die in one round or two at the most. We've had maybe like 1 or 2 challenging fights in 5 months.
There're a few quests that we are ostensibly doing, but he doesn't use simple things like "okay, here's a plot hook that leads you somewhere". There're no tables he rolls on, he doesn't use CR to figure out encounter difficulty, his NPCs are extremely unhelpful, our group has no real reason to be together, and the lore of his world (future apocalypse) doesn't make much sense with high fantasy characters who are half-orc, aasimar, high elf, and forest gnomes. We seem totally out of place but no NPC seems to notice.
This feels more like a disconnect between what your expectations are of the game (plot hooks and pregenerated stories) and the DM's style. A wide open sandbox can be a fun game. I'm half running one myself, with the "plot" essentially being the lives of the players and what they decide to do rather than something I'm foisting on them.
But, from some of the other points, it does sound like he's a little rougher in his execution.
I recently introduced him to Critical Role and I think that is honestly the first D&D game besides ours he's ever seen. He even remarked afterwards that he felt insecure about his own campaign after watching it after seeing how different our game is from theirs. I don't think he realizes just how bad he is, and he seems resistant to 5e resources intended to help people like him get better.
In fairness, I'm an experienced gamer with a couple decades of Dungeon Mastering experience, and Critical Role makes me feel insecure at times.
Forwarding a few more D&D games might also be a good idea. There are a bunch on the
D&D feed. There's Dice, Camera, Action, the two Maze Arcana games, and Dragon Friends. Or something like Girls, Guts, Glory. One of which might be less intimidating. Really, showing him a few different styles of DM and different ways of playing might do more than showing him just Critical Role.
I've been carrying the group in terms of encouraging we roll using our skills for things, or using a rule from the PHB when it would apply, and he just sits back and lets us do all the rules lawyering, waiting for us to tell him how to run the game.
Which can work fine. I've been in multiple games where one player knows the rules better than the GM and is the designated "rules monkey", adjudicating rulings and looking up the answers to questions so the Dungeon Master can keep the game running.
And I've run a few games where I've known the system a little less than the players and had to turn to them for clarifications.
Looking at everything, I agree with the others that say you should move on to a new game. Partially because the DM has his weaknesses and seems unwilling to work towards improving as a DM, which is not a good sign.
But mostly because what you want from the game seems to be very different from what the DM wants from the game and the type of campaign they seem interested in running. And that's going to be an issue even if they learn the rules and become better at handling combats and conflicts. In fact, if they
do get a better handle of the rules, it will just augment your perceptions of the tonal differences between your expectations and their presentation.
