I agree with you more than I can possibly explain. It's so annoying whenever the DM (in DnD or any other game) just gives you the answers to a puzzle (unless asked of course). I'd much rather try and figure it out, or come up with some other far less nonsensical solution (Hey, who said a giant spiked boulders filled with crossbows was a bad idea?)

When it comes to monsters and their ability, a lot of metagaming goes on there because the players have likely seen the creature in another campaign or simply know about it from DMing or some other source. You can only hope that they limit their perspective to approach it properly. There is one guy in the game I'm currently playing that can't seem to separate that kind of thing.
Amusingly, the character I play in that same campaign is an attempt at me being absurdly naive. He's a warforged Artificer...with a 6 wisdom. The idea was to play him sort of like Data from TNG; Able to learn, but still doesn't know about a lot of things. He routinely blunders into things improperly, but often does what he needs to. Just don't ask him to do triage, it's a dangerous thing given his experiences XD

I agree. However, when I DM, if the players spin their wheels for a long time, looking for that key thing they missed that will advance the main plot, and it seems like the fun level is dropping, I try to provide more hints, or come up with an alternative path on the spur of the moment. I let them go off on tangents, or when they think their one real friend in the world is the BBEG (hilarity ensues), but as soon as I get the sense that the fun is deflating, I try to turn it around quick.

On the flip side, tomorrow the game where I am a player, we invade the ruins of Rhest in the Red Hand of Doom. We think we have a good, unique plan. And our DM doesn't cut us a lot of slack (though one time he did turn a near-TPK into a 1/3 PK... other than that, he a hard-ass.) So I am hoping he sees the pure awesome of our plan and plays the enemies that way, and that he continues to be unforgiving if we screw up.

When it comes to DMing, there are several different ways to roll. In Anon's comment above, the reason the "red hand of doom" game is fun is because the DM is consistently a challenge, so the players expect that they will die if they mess up.

For my players, I've typically found that the most fun comes from the problem solving situations, and that with some thinking you can feel like you've handed the answers to your players, but only half of them will have actually figured it out, and that half feels its so obvious that they won't bother to inform the other half, who is blindly trying to figure out what to do. When things really get stuck, I will give them a hand, though, usually in exchange for some sort of check (knowledge or wisdom, depending on the situation.)

I've been reading through the Mouse Guard rules, and there's a mechanic I really like. Give them the victory, but with a twist. "You miraculously kill the bad guys, but you lost all your food." "You miraculously find the hidden door, but a stench filled wind blows out all your torches." It gives them the victory, keeps them (more-or-less) on track, but gives them a handicap.