3.5 was edition I played the most. It was a reason why I quit RPGs for nearly a decade because I hated it so much.
Every time I see another meme about how amazing 3.5 Tarrasque is, I remmember how amogn actual 3.5 players Tarrasque was the biggest joke. It was always brought up as definite proof designers have no idea how to make good monster. It was laughably easy to beat. A wizard could casually solo it, the same abilities people now miss in 3.5 amounted to ribbons. It was a laughingstock, forums had 100+ pages discussions how to fix it and general consensus was it';s beyond saving. It was first proof in 3.5 if you cannot use magic you're only good to roll over and die.
I honestly don't know if everyone claiming 3.5 Tarrasque is such a horrifying monster are trying to rewrite history or unintentionally proving what a broken, unplayable pile of garbage 3.5 was, if it's biggest punching bag is actually dangerous in a different, better designed game.
In 5e it's quite hard to find the rules for "stat reduced to zero", however the only stat that causes instant death at zero is CON.
Given that stat drain isn't that common in 5e I'd hope the effects are described as part of the ability, for instance for the shadow:
Yes.
5e very often puts caveats into the rules text for an item/spell/monster, and they very often don't match the "generic rule". The advantage here is that you shouldn't have to cross-reference stuff as often to know what's happening. The disadvantage is that, because you don't ever reference the generic rule, people often don't know it even exists.