the trap card -divine wrath-
Yes it can. Sangan is a triggered effect, Stardust Dragon Assault Mode can chain to and negate it.
Yes, Sangan's mandatory trigger will activate after the monster is summoned.
Yes, Sangan has a Mandatory Trigger (so never misses the timing), and a tribute is a form of Send. If you tribute it for a tribute summon, Sangan will activate when the summon is successful, or if the summon is negated, after the resolution of the negation card. If you tribute it for a card effect such as Enemy Controller, then allow the chain to resolve. Sangan will start a new chain as chain link 1.
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.
No, Power Tool Dragon has no such negation effect.
Yes, it does because its effect is activated in the graveyard, similar to Sangan and emissary of darkness.
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.
The population of Sangan-e Olya is 171.
No
No part of Call of the Haunted or Royal Decree affect a monster's ability to attack. The Sangan will be able to attack as normal.
Sanwitchis the Fusion monster made from Sangan and Witch of the Black Forest.
It will activate no matter where it was sent from. If it had to be from the field, it would say so - like Sangan does.