Sangan triggers in the graveyard, so it's irrelevant if it was face down or face up when it was destroyed. It will trigger in both cases.
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If "Harpie Lady 3" is destroyed while face-down by the effect of any LV "Mystic Swordsman" or "Sasuke Samurai", it's effect will not work since it was not flipped face-up. If it was attacked while face-down, it is flipped face-up and after damage calculation, it's effect will activate.
No monster can activiate its effect while face down unless it specifically says so; only face up.If you are referring to monsters who say their effects activate when Flip Summoned, that means you must flip the monster up manually during your Main Phase after it is set face down. A monster fliped face up from an attack does not count as a Flip Summon.
Call of the Haunted will resolve first, summoning Sangan. Mystical Space Typhoon will resolve second, destroying Call of the Haunted. This in turn will destroy Sangan. Sangan will start a new chain with his triggered effect and search for a card of 1500 ATK or less.
No, flip effect activate when the card is flipped, which will be by Flip Summon, or being attacked, or flipped by an effect. Simply being destroyed while face down, will not 'flip' the monster.
Flip effects will activate if flipped manually by Flip Summon, or when attacked. Also must include "FLIP" in all caps for its effect to activate, or say 'when this card is turned face-up'. For example if a monster such as Guardian Sphinx is flipped face up by an attack or an effect (spell, trap or monster), the effect does not activate, because only a Flip Summon triggers it, not a generic flip. When a card effect destroys a face-down monster, the monster is destroyed and flip effect isn't activated because the monster never flips. Mystic Swordsman Lvl. 4 destroys the monster it attacks without flipping it, so a Flip Effect monster attacked by it will not get its flip effect. To summarize, if a FLIP effect monster is attacked while face down, then it will activate. But if it's destroyed by a card effect while face down then it won't activate. Some card effects let you flip monsters face up and let the flip effect activate, like book of taiyou. But others, like ceasefire don't let it activate. If it says 'when this card is flipped face up' then you have to do that manually on your own turn.