When the thief ends his movement on a dark tile, he can examine the dark tile. Does that mean that he has to end his movement for the turn in order to perform this ability, or can he move from dark tile to dark tile, peeking at each dark tile, as long as he has movement points available?
You can only peek when all movement is done, i.e. at the end of your turn.
Does the thief have to end all of his movement on the entrance tile in order to stash treasure? Can the thief pass through the entrance tile, stash treasure, and continue moving as long as he has movement points available?
No, you can continue your turn after stashing treasure.