I just realized we have a guide on Steam but not here. I'll post it in this comment below:
To unlock all 3 special scenes, you need at least 2 play throughs
Fist time: To unlock Duy Khanh and Lan scenes
To unlock Duy Khanh scene, experience all bad endings
Bad endings:
Chapter 3: Punish him
Chapter 8: Deny caligraphy request
Chapter 11: Accept proposal
Chapter 12: Start a war
Chapter 14: Seize him
Chapter 18: Refuse offer
Chapter 19: Order the court to ignore issue
To unlock Lan scene
Chapter 22:
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Say no to the date
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Observe him bath
Second time: To unlock Minh Quang scene
Chap 1: Follow him
Chapter 16: Join him to the streets
Chapter 22: Agree to go on date