So, after some time I came back to playing live (not online) RPG because a friend of mine, who is used to D&D 3.5, asked me to help him with a 5e table where almost all the players are new to D&D (most have played other systems before though).
The thing is: both sides seem to be confusing what is their role in the game. For example, the very first narration from the DM forced movements on a player character (the DM moved the PC himself, instead of the player describing where she wanted the character to go). Another example is that the DM constantly narrated how the characters felt, e.g., "you are scared", "you trust this person" (when they rolled a bad insight roll against a high deception roll), etc.
Similarly, the players frequently argue whether or not an NPC should behave like it did, which slowed the playing pace considerably. The players also seem to have some problem with suspension of disbelief - or simply trusting the DM - complaining about how something happened. For example, a maid NPC appeared "out of nowhere" and the players wasted minutes complaining about how their characters didn't perceive the NPC passing through them before (which could easily be a teleportation magic, an illusion, the NPC simply having had a really good stealth roll, or an infinite number of other explanations).
By itself I don't think it would be a problem if everyone was having fun, but as I mentioned, my main concern is that these arguments are slowing down the play just too much. Additionally, it's noticeable that everyone is getting a little frustrated over everything.
The DM ended up resorting to (a bad, IMO) in-game solution (which was to knock out the PC of the player slowing down the game for a few in-game hours) so the story could continue, but besides being extremely temporary, it also (rightfully, I guess) frustrated the player more.
For clarification, the DM has no intent of screwing with the players; from what I understand, he does this in order to move the story forward. The players, on the other hand, feel that everything that does not go according to their expectations/plans is the DM trying to screw them, and waste too much time arguing about that.
In short, how can I gently remind them that the players' role is to describe their character actions and feelings (and the DM should avoid interfering in this part), while the DM's role is to describe the environment, consequences of the actions and the behavior of NPCs (and the players should probably trust that if the DM said something happened, then something happened, and not waste half an hour in an argument about that being impossible, unfair or whatever).
Additional details on background
I feel that this might be related to their previous RPG experiences which involved a little of the old "DM vs. Players" dynamic. That's why sometimes the DM seems to think he should force the PCs to do something (not trusting that the player has the honesty/ability to play accordingly to what makes more sense)1 and the players feel that everything is an evil plan from the DM to kill their characters.2
If it is relevant, the adventure is a homebrew one (based on a book the DM is writing).
The players are all 20–30 years old, except for one woman who is 19 (and possibly the least problematic one - she's very calm, with experience in 5e).
1 More details on an example already mentioned: an NPC lied to the PC. That particular PC didn't have any kind of a priori information to know that it was a lie (although other PCs had, thus the player had) and rolled a really bad Insight check. The DM immediately narrated it as "You trust him!". The player agreed - and he was going to role-play as that anyway, i.e., there was no reason for the DM to force that upon the player/character.
2 The NPC that "appeared out of nowhere", that the players wasted minutes arguing about, was actually an ally. They were worried that the NPC appeared behind them because they thought they were getting assassinated. In the end she was just an ally that was watching them closely to learn if she could trust them and help them if needed, eventually. She decided to leave the shadows when she thought there was enough evidence that the PCs were trustworthy.