A friendly tip on posting: Add your question to the end of the existing help thread. There is no need to start a new thread for each and every question.
One way of getting off the balcony is to use the vase.
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×You can just climb down the wall, use the hand icon on the wall below the right hand side of the balcony. But first you need to deal with that guard.
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×Drop the vase on his head.
Regarding the rope, you can still play all the way through the game if you don't have it. You just don't get the best ending. I would recommend playing through the whole game once, just to get the basics. Then play again to optimize your final score, once you're oriented. You should also be aware that there are multiple solutions to many of the puzzles in the game. Just because one person posts about solving a problem in a certain way doesn't mean that
you should solve it that way.
Where the alarum is:
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×It's a rope you pull in the upstairs hallway of the castle.