As for the other things, I don't subscribe to the "gotchas are bad" take that seems so prevalent here. Sometimes you're just gonna be "got", be it through bad luck, inattention to detail, or simply that the dungeon element beat you.
I agree with "inattention to detail". Which to me is synonymous with "the dungeon element beat you".
"Bad luck", however, sounds suspiciously like "screwed by RNG", and that I don't agree with. The only reason I like dice rolling in combat is that the outcome is typically the result of a lot of dice rolls, so good and bad luck tend to balance out, and if the encounter is well-designed it's the player decisions that really matter.
But rolling a single d20 where N or greater means "you don't take any damage" and below N means "you take 1d8 damage"? That's just pointless, except maybe for the nostalgia value of playing the way we did in 1980.
Attempting to discover secrets should be 100% player. Success in such discoveries shouldn't be nearly so guaranteed, though, and sometimes failing to discover a secret (or not even bothering to look for it) means the secret is going to reveal itself in a quite unpleasant manner.
Yeah, hard disagree. If you look in the right place (or otherwise do the "right" thing, whatever that means and whatever the tells suggested) then in my game you find the trap. But searching takes time, and
time is money, friend.
I also don't use dice rolls* when there's no consequence to failure, with stakes understood by the player. (And, no, failing to detect the trap is not a consequence of failure because you're still in the same state you were in before making the attempt.)
Confession: it's really hard to break decades of habit, so sometimes I still call for dice rolls for finding traps or knowing a fact or whatever. But I am constantly striving to get better at it.