The gnoll is „Savage“, but only when it can see two other creatures with the Savage trait within 30 feet. Why? Why is the gnoll incapable of attacking with all his savagery, when he fights alone and is up against a helpless victim? Is he somehow restrained in his rage when he is alone?
Yes. Gnolls are stereotypical pack animals - that is, savage in packs and cowards alone.
Continuing with the Hobgoblin, it has the „Steadfast“ trait, meaning it cannot be frightened while an ally is within 30 feet. Why not? This may make sense when the Hobgoblins encounter the Player Characters, but does it make sense when two Hobgoblins encounter Cthulhu?
I could pose the same question in relation to a dwarf: if it travels through time to the modern world, and chows down some plutonium, is it immune to the toxic effect? I don't think the D&Dnext rules are intended to model these sorts of extreme cases. (Anymore than, for example, it models combat between two ants, or two housecats.)
In addition, one could always rule that Cthulhu does not impose the "frightened" condition, but some more mindblasting effect to which hobgoblins are not immune.
The same with other traits and actions like „Commander“, „Protector“ and 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).
Commander is pretty clear: the hobgoblin captain gives commands, which help the other hobgoblins in their fighting.
Armour Piercing is also pretty clear. Normally, a hit vs AC 10 would hit the armour but not penetrate it; while a hit vs the target's actual AC would not only hit the armour but penetrate it. (Roger Musson discussed this in an early number of White Dwarf, in an article called How to Lose Hit Points and Survive, but I doubt that he was the first to notice it.) The minotaur is so tough that all its attacks penetrate armour to some extent: hence the descriptor "armour piercing", and the minimum damage on any hit vs AC 10.
If you wanted to make action resolution more complex, you could make the minotaur's minimum target number AC 10 + DEX component of the target's AC. Given that comparatively few PCs with a high DEX component to AC are going to be trading blows with a minotaur, the designers may have though that the extra complexity was not worth the effort.
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?
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I’d prefer an approach where the Halfling can always take a second Save against fear effects or something like that, as it wouldn’t force the player to play out how his Halfling shakes off his fear, when it’s really hard to explain how that would look like. And even harder to explain why he couldn’t have done it earlier.
The reason the halfling couldn't have done it earlier is presumably because (as others have posted upthread) it takes time and effort. The halfing is mustering his/her resolve. What does it look like? Pick your favourite scene from LotR - maybe Merry deciding to stab the Nazgul, or Pippin deciding to pledge fealty to Denethor.
The problem I see here is that "a character realizing that he can act despite his fear" should not be represented as an action in a six second turn sequence
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It brings up difficult questions such as: Why couldn't the character just realize that he can act despite of his fear when he was first affected by the fear effect? Does it really take him six seconds to come to this realization?
The simpe answer, surely, is Yes, it really does. Maybe it's an idiosyncracy of halfling psychological processes.
What I dislike considering associated or dissociated mechanics is the fact that you can cast some spells as Rituals and others not. This seems to be tacked on from the designer's point of view but it is hard to explain from the POV of a character that lives in the D&D world.
Surely here, of all places, the "it's magic" explanation will do! Some spells admit of being reduced to ritual formulae. Others don't. Why? Well, once you have a general theory of how magic works, you can add on the epicycles to explain how some admit of ritualisation and others don't.
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.
Because it's part of the spell effect. Maybe the spell requires speaking very few words, or only a very simple hand gesture, or maybe it has a haste effect built into it.
Again, "it's magic" seems like it might be enough here.
a player could always confront his/her DM with questions such as „So you’re telling me I can cast Battle Psalm, a 2nd Level enchanment, and attack in the same round, but I can’t do the same with Radiant Lance, a Minor evocation?“
Mightn't part of the answer that what makes Radiant Lance minor rather than 2nd level is precisely that more time is spent casting it: you can do it repeatedly, provided you say the full rites and make all the right gesticulations every time.