I really had to rush through the rules to play for the first time as a Keeper for my firends.
But I got a load of questions that I had a hard time answering.
They might be in the rules, if so I have missed them.

So basic I understand that an explorer can do 2 steps one action.

1. can the explorer do it in ANY order? like :step, explore, step or explore, step ,step. Or has it to be step, step, explore?
To clarify: as soon as you've explored/done an action your round is over?

2.1: Encountering a puzzle, evrytime you try a puzzle you are stuck right? You cannot move or anything?
After tryinga puzzle (wwither you have discovered it or not) your turn is over right?

2.2: if you solve the puzzle have you used an action, or can you enter the rome and "explore"?

3. Enchountering locked doors:
So lets say that the first round you stand in a hallway at the ned of your turn. Next round you, for your first step, try to enter a room. Its revealed and locked.
Have your turned ENDED or can you do anything esle?
Did it cost a step, or did it cost an action to try to enter it?

3. Unlocking doors, its similiar. I guess that unlocking a door with a key kost one action right? and you enter the room (for one step?) or is that action both unlocking and taking the step?

So you know that this is the Arkham Horror Board and there is a separate board for Mansions of Madness?

Although I am sure someone here could help you out, you might have better luck over there to get a quick answer ...

Man, as Schwaig said, it seems like you rushed through the forum as well. No place for Mansions here, but Arkham Horror.

Anyway, all your questions are in the rules.

a) you may indeed choose to perform an action (exploring is just an example of a wider array of possible actions, from using items to perform a combat check and so on) first and then resolve your two movement steps, or move first and then perform your action and then move again, or go for a move-move-action. You decide

b) being "stuck" means nothing in game terms. You have to solve the puzzle to complete the specific action / movement the puzzle is blocking. So, if you are exploring a room and you're asked to complete a puzzle to explore further, you cannot explore further unless you complete the puzzle. This doesn't mean you are forced to stay there. If you try the puzzle, fail and then have move left, you can move away

c) doors and locks hinder your movement, and have nothing to do with actions. You try to open a door, it's locked, resolve the lock condition on the card, if you pass you enter the room, if you fail that move step is spent and have to do something else now. Exploring the room has nothing to do with locks

Hope this helps