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.
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What's in italics is answering your question. The rest is just other helpful information. Answer from yugioh-card.com: If Ultimate Offering is face-up, you can activate its effect multiple times in the same chain.When you activate Ultimate Offering's effect, you pay the 500 Life Points as a cost at activation, and then the Summon occurs at resolution of Ultimate Offering's effect in that chain. This means that it is possible to Summon a monster in the middle of a chain with Ultimate Offering's effect.If you are using Ultimate Offering's effect to perform a Tribute Summon, you Tribute the monster when Ultimate Offering's effect RESOLVES and you perform the Tribute Summon, NOT when you activate Ultimate Offering's effect and pay the 500 Life Points.If your opponent activates a Trap Card, you can chain the effect of your face-up Ultimate Offering to the Trap Card to Tribute Summon Jinzo (if you had a monster on the field to Tribute) and negate the Trap Card's effect.You cannot flip Ultimate Offering face-up AND use its effect in the same chain; you must have Ultimate Offering face-up on the field before the current chain began.If you activate Ultimate Offering's effect to Summon, and your opponent chains Mystical Space Typhoon to destroy Ultimate Offering, the Summon does not resolve because Ultimate Offering is a Continuous Trap Card and is no longer on the field.You can activate the effect of a face-up "Ultimate Offering" during your Main Phase even if you have not done a Normal Summon yet this turn.
Yes. Because Kaiser Sea Horse allows you to use it for 2 tributes for a Light monster and Gilford the Lightning is Light, you can tribute Kaiser Sea Horse plus one more monster to Tribute Summon Gilford the Lightning.
No. The material monsters are no longer considered 'on the field' and none of their effects are active.Because they are not considered to be on the field, effects that specifically trigger when they go from field to graveyard will not activate either. For example if a Sangan is an XYZ material, it will not trigger its monster search effect when it goes to the graveyard.However if the monster does not say it has to come from the field, such as Dandylion, then these effects will trigger when they go to the graveyard.
No, you do not 'tribute' the Synchro Material for a Synchro Summon. They are sent to the graveyard, not tributed. You can tribute an opponents synchro monster for "Assault Mode Activate!" to summon the assault mode monster from your deck.
Yes, the monster obtained by the effect of Creature Swapcan be tributed.