My apologies of all of the following has already been said:
From the Bestiary:
„Mob tactics“. In the description it says that the creature chooses an opponent. Other allies that also have this trait gain a bonus to their attack and damage against the chosen opponent. However, there is no explanation of what is happening and I’m struggling to find an answer.
Picture a mob ganging up on someone. They attack from all sides, one holds him while the others punch him, one knocks him down and the others stomp him. What he's doing might be as simple as growling "get him" then makes an aggressive, but easily defended against attack to absorb his attention while his buddies move in on his unprotected back, or it might be some choreographed series of cooperative maneuvers where they support eachother.
The gnoll is „Savage“, but only when it can see two other creatures with the Savage trait within 30 feet. Why?
Gnoll psychology as pack animals?
The Hobgoblin has a „Disciplined“ action. It chooses a foe within it’s reach, and the next attack against this foe from his ally has advantage. But what is the Hobgoblin doing?
Executing some well-drilled maneuver in coordination with his ally, no doubt. Roman legionaries, for instance, would use their shields to block the foe directly in front of them, but attack the enemies to their /right/, for instance.
Continuing with the Hobgoblin, it has the „Steadfast“ trait, meaning it cannot be frightened while an ally is within 30 feet. Why not?
Not wanting to show fear in front of his comrades?
the minotaurs „Armor Pearcing 4“ where the minotaur’s foe takes damage even though he wasn’t hit from the attack (something which I personally can’t stand).
Damage on a miss, much like damage on a hit, can be a matter of more than just actual wounds. An attack could be so brutal or aggressive that even if you avoid the brunt of it, you still expend some of that precious luck/skill/etc, or still get battered a little even though you got your shield in the way in time. That's just hps.
The Halfling can move through spaces of creatures that are larger than it. I find it awkward to accept that every Halfling in the world could do this against every larger creature.
Meh. That's a matter of scope and abstraction. 'Halfling Nimbleness' could work only for most halflings, only vs certain creatures, only in certain circumstances, with every creature, circumstance, and halfling prerequisite (height, DEX, whatever) all detailed, but it'd be far more rules than such a modest ability calls for.
Also, the Stout Halfing’s „Fearless“, where he takes an action to end the frightened condition. What action does the Halfling take and how does it look like? I don’t like it when the rules tell us that something is an action when it isn’t really an action.
It's instead of an action. You're frightened, but rather than staying frightened you fight through it.
Spells:
What I dislike considering associated or dissociated mechanics is the fact that you can cast some spells as Rituals and others not.
Well, some spells would be pretty worthless with a ritual casting time - like any combat spell. I'm going to put you all to sleep! Just wait while I get out my 50 gp of material components and chant for 5 minutes. Might as well make 'em some warm milk or valerian tea.
I’m also having a hard time to accept that some spells can be cast in rounds where the caster also does some other action. If I was a caster I would ask myself why I can't cast my other spells and also do something else during the casting.
Some spells are presumably shorter and/or easier than others.
I dislike that some spells only affect creatures with a certain hit point maximum. I wish my players wouldn’t have to wonder about how many hit points the monsters have (or Hit Dice, which, although closer to how old editions of D&D did it, I wouldn’t find much of an improvement).
Yeah, it's prettymuch a return to the HD limits of classic D&D. The sense of it isn't hard to see, though: if a monster can resist being beaten to mush by dwarves with giant hammers, it can resist being turned to mush by magic.
Having to think about Hit Point breaks the player’s immersion and tells them to think about monsters from a „we’re playing a game and this is my opponent“ point of view.
That's a problem with hit points, yes. If you can't handle the abstraction of hps - which, really a sort of ablative 'plot armor,' and 'narrativist' and dissociative as all heck - then D&D was probably never your game.
The Fighter:
This iteration of the D&D Fighter, in comparison, can only make the combat maneuvers that he has mastered by aquiring them with a feat.
I'm not sure it's a feat, exactly, Fighting Styles follow the same pattern as Specialities, which are collections of feats, though, so maybe it is?
Doesn't sound too dissociative, though: you can do the things you've trained to do, not the things you haven't.