This is not my experience. DMs make calls all the time. However, if the rules say "Magic Missile always hits" then they aren't expecting the DM to suddenly ask for an attack roll when they cast the spell. And if they are sneaking, they don't expect the DM to declare "and the guards sound the alarm" without allowing you the chance to succeed.
Well, it's common in many other NS style games. The NS games, even more the players, want everything by the rules and dice....not the DM's whims.
And the second part is another good difference:
Old School: anything anywhere anytime might happen regardless of what the character does or does not do. And very often the character...and player..will never know the how or why of anything that happens or does not happen......ever. And there is no "chance" for the player and character always.
New School: It's rare for anything to happen with out the direct input of a PC. The players expect to be informed of things, much like they are an audience. The DM quite often will just answer nearly everything OOC for the players. And more often then not, the DM will give the PC a change to do something always.
Well... yeah? This gets into the idea of informed decisions. To give an IRL example, I was once playing a Storm Sorcerer who was in a fight with a Dracolich. I had spent multiple rounds of combat blasting this thing to kingdom come, and at one point mentioned to a party member (because I was tracking) "We've done over 500 points of damage to this thing, it has to be close to dead." and the DM was confused on why I thought that. I mentioned that, my character alone had rolled almost 300 damage from his attacks... which is when the DM told me this was a Blue Dracolich and immune to lightning. He had never described that the dracolich had blue scales (he'd forgotten) or that it wasn't reacting to my attacks. Which turned an epic fight into a sour memory of wasting my time and energy for nothing.
I guess your example is a good example of a bad DM that forget to tell the players something. Though this has nothing to do with what I mentioned.
Players cannot react to or notice information that is not provided by the DM. And it feels very much like a betrayal when a DM has something directly affect the Character without any knowledge, or have them automatically fail or be affected by something without a save.
Old School is more about the detail overload. The players are given all the details, but the player has to use their own skills to find the relevant or important information. New School is more about focused details. The DM as a fan of the players highlights the details the players need to know.
And as said above: Old School anything can happen to a character at any time with no warning, no chance to do something or a save. Though the DM can give one if they want. New School the DM as a fan will nearly always give a warning, give a chance and a save.
Not in my experience. In my experience it is far more about reliability. My character can skin a wolf and cook its meat, don't need an ability on the character sheet. But if I have an option between using the shield bash shove from my feat, or attempting to throw a looped rope around an enemy's feet to trip them and knock them prone... I'm going to use the shield bash, because I know how it works and what it entails.
So...like I said. A NS player sticks to the rules they know.
That's ... really misleading. Saying that character choices and builds is more important than the ability of the player to rattle off a convincing argument does not in negate player decisions and declared actions.
I don't really understand your comment? Can you elaborate more?
Though it can also be so broad as to be of questionable value. As used by the hardcore types, "Old School" is a moderately useful label, but "New School" not so much because its basically "everything not Old School".
Well, until there is a New School that makes the old new school Middle School.