Yes it will work also it can work with special and tribute summons as well
it will also work if the oppenent plays a monster on his-her side of the field
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If a monster is set you cannot activate it. "Torrential Tribute" can only activate when any player performs a flip summon, normal summon, Ritual summon, Fusion summon or Special summon, but a set is different from a summon so you cannot activate "Torrential Tribute". The same applies to other cards that activate when a monster is summoned (like "Bottomless Trap Hole" and "Solemn Judgment").
You can definitely tribute a monster on the same turn as a Normal Summon, ie, you can normal summon Exiled Force and tribute it for its effect. What you can't do is tribute it for a Tribute Summon because this is another Normal Summon, you can't perform two in a turn unless an effect allows you to do so. But you can tribute that monster for other things, like an activation cost or for a special summon.
Yes, you can tribute monsters for card effects and Tribute Summon the same turn you summon a monster. However, you cannot Normal Summon a monster and Tribute Summon on the same turn because you can only Normal Summon once per turn. Cards such as Double Summon and Ultimate Offering will let you do that.
No, a Tribute Summon follows the same position rules as a Normal Summon, so a monster you Tribute Summon is either face-up attack or Tribute Set into face-down defense.
El Shaddoll Fusion doesn't affect how Torrential Tribute resolves. Imagine you summon a monster, and the opponent responds with Torrential Tribute. You chain El Shaddoll Fusion. When that resolves, it lets you perform a Fusion Summon as written. But Torrential Tribute was still correctly activated, and when it resolves it will destroy all monsters on the field - it doesn't matter that the monsters have changed and are different from the ones present when it was activated.