See, I don't fully disagree with you, but I find it weird that the DM giving out numbers and technical information is fine, but the players seeking to confirm those same numbers and technical information isn't.
It's D&D. the DM still has to say how much damage is sustained, it's the bare minimal technical information to be conveyed from him to a player. What he is not saying is "and out of this, it's one or more attacks, with such and such bonus and sneak and hunter's mark...".
I just don't get where "trust" is coming into this. It doesn't sound like the player thinks the DM is lying, they are just trying to understand what they are being told. If they didn't trust the DM... why would they bother asking? They wouldn't trust him or her to give them a real answer.
Damage and Hit Points are abstract counters in D&D anyway. For me, that kind of verification is quite often based on some sort of mistrust and checking that the DM has not forgotten anything about the defenses of the player. Now, coming back to the original post, it's clearly that "To him, we're playing a wargame with certain rules and there's a bias towards "perfect information" and that might be less a question of trust, but I have addressed this point separately.
I also have had a lot of DMs, even experienced ones, mess up the rules.
And for me, it's in general not a problem. Of course, if it's all the time, and it screws up the vision of the universe because it's inconsistent, or if it's done on purpose to make the world seem more dangerous and in a sense screwing the players, it's bad, but I've almost never met that kind of case, especially the second one. And the first one is usually linked to an inexperienced DM.
But if once in a long while you take a bit more or a bit less damage, who cares ? For us, it's not worth interrupting the flow of the game for a technical discussion leading to ruleslawyering. If really it bothers you, wait until the end of the session and ask the DM about confirmation that something works one way or another, and if oyu don't go into accusatory mode, and the DM feels like explaining (he might not, by the way, as is his perfect right, in particular if the player has no reason to know about it - special magic, special NPC, special circumstances), discuss about it.
Misremembering something like Charm being a one I've encountered a lot, and while I know a lot of people prefer to project the DM as infallible, or that correcting them ruins the game because they might be doing something they homebrewed... sometimes a mistake is a mistake. And it isn't wrong to make sure if it is homebrew or an honest mistake. DMs shouldn't feel attacked by that.
It all depends on the way it's presented, see above. It might be a mistake, or it might not, and it's not a good thing, in my view, to encourage discussion of things which might or might not be mistakes during the game. Again, it might depend on your table etiquette and wishes, if at table the players went to go into wargaming style where everything is justified, that's cool, but it's also cool to let the story flow without peppering the DM with questions and without making the game technical, it does not need to be.
Not pulled what? Making a mistake?
Either cheating or making a mistake of that size. You see, when there is trust, the players are also careful to avoid breaking that trust, so they will not do anything outrageous without checking, usually quietly between themselves if their understanding is correct, or with the DM before pulling it off.
It also goes with the "not breaking the flow of the game", pulling something outrageous will always to this. If it's justified, it will be fantastic, and everyone will applaud, if it's unjustified or really borderline (in particular in terms of interpretation), might as well double check before pulling it off. And I think that this is why it has not happened in years (or more exactly, it happened about 3 years ago with the last real powergamer at our table before he left the table by mutual agreement, but it has not happened in much longer with the other players, at all the tables of our groups).