By Ringeltree
 

I think all three parts of my explanation got through, but I'm not sure. Let me know if they didn't.

By Ringeltree
 

Since they provide contradicting instructions, exactly one is telling the truth. The 3rd and 4th agree that the red key is first, so are both liars. The 2nd is telling the truth and describes the path to the door.

By Ringeltree
 

Character 3 says:
You must use a red key, and you must use a yellow key.
You must use the red key first.

Character 4 says:
You must use a blue key, and you must use a red key.
You must use the red key first.

By Ringeltree
 

The second puzzle works like this:

The statement 'all of us lie' must be a lie. So at least one is telling the truth. Character 1 is a liar.


Character 2 says:
You must use a yellow key and you must use a green key.
You must use the yellow key first.

By Ringeltree
 

Ah. I see. I'm running the logic puzzle that these statements never change. So the same logic applies to the third puzzle.

By Ringeltree
 

In A little AI trouble, in the second puzzle, each makes exactly two statements. The one that claims to always lie must sometimes tell the truth. Since one statement is false, the other (the claim about the exit) is true.