Some 5E DMing questions.

I'm still not 100% clear about how detecting traps and hidden things work and I'll probably have other questions.



Scenario 1:

Character walks down a set of stairs, a trap is on the stairs but he's not looking specifically for traps.

Game mechanically how is this dealt with?

Is this some sort of roll vs Passive perception or something for some sort of chance to detect the trap?



Scenario 2:

Character walks down a set of stairs, a trap is on the stairs and the Character is looking for traps.

how does that work?

A perception(Wisdom) check? vs the trap difficulty to detect?



Scenario 3:

character walks into a room, there's a secret door.

He's not looking for a secret door.

What's the mechanics for a possibility of him detecting it?

another passive perception check?



Scenario 4:

character walks into a room, there's a secret door.

He's looking for a secret door.

how does this work?

The dungeon delver feat implies it's either Perception(Wisdom) or Investigation(Intelligence) to find it.



Scenario 5:

Character walks down stairs, finds a trap, it's not set off.

He doesn't have the thieves tools usage skill. can he still make a DEX check to disable it?



Thanx in advance.

Some 5E DMing questions.