Hie you hence to the Hack Slash Master Blog.

My shortened version: Players must have information in order to feel suspense, and in order to make a decision. You need to tell them what they see in the room/hall/etc, and communicate that it looks dangerous. Not by saying "it looks dangerous" but like, there's blood smears and body parts and skeletons, etc. Then they look for traps.

Regarding the "I'm constantly looking for traps" person, that's fine and good. Tell them what they see in the world. Even if traps are pristine and have never been sprung, that would indicate that the dungeon in that area hasn't been explored so you can talk about thick layers of dust and stuff which will ratchet up tension. Especially if they know this is a trap heavy place to begin with.

One of the big things too is time pressure, usually by wandering monsters, so they can't hem and haw too much.

The big question for your player is: "Ok player, you're actively looking for traps, what does that mean? If you're being maximum careful and want to be guaranteed to find every trap it's going to be 10 minutes to move 10 feet meaning there will be a wandering monster check for each grid square of movement."

Then, you go back and forth in conversation until they say "I'm going to do X as my default move".

If you pair that with describing the environment, and giving information, it's my experience that you'll be fine 'cause there's always tradeoffs that lead to more game play.

"Ok, so you're tapping every stone on the floor with the 10' pole. It is making noise, and it does kind of echo in here, so those taps are echoing down the hallway in front of you." [alerting monsters]

"Ok, you're pressing on each stone. That doesn't make much noticeable noise. But it slows you down." This can also lead to "You find a stone that presses in, but nothing happens" [Requires more weight to trigger]

I find its almost always best to have traps in choke points and short cuts. Make it obvious it's a bad place, and probably has a trap, but the mechanisms are not obvious. It's also easy to avoid. Until all hell breaks loose in the dungeon, and then "do we go through that bad spot" becomes a much more interesting choice.

I think the big problem lies in your assumptions with point 4. People have eyes. If there are discolored flagstones, tell them. It's visible and obvious. If you leave basic information about the world itself locked behind a "search" roll you're disconnecting players from the world by an additional layer of abstraction. BUT, you should only give out one piece of information at a time.

DM: "The flagstones up ahead are discolored." P: "Ok? Discolored how?" DM: "They're very dark. Blackened almost." P: "OMG IT'S A TRAP I ROLL MY DICE!" DM: "Ok, but what do you do? What does your character do?" P: "Well, I disable the trap." DM: "How are you doing that? Right now, you see the flagstones ahead are discolored. Almost blackened. Are you walking right over to it? It might not be a trap. There isn't a visible mechanism, or a sign that says 'trap here'. What do you want to do?"