You can never tribute something you don't control unless the effect specifically lets you.
So Soul Exchange, Trap Eater, Lava Golem are all examples of something that allow you to tribute your opponent's cards, and they all clearly say so.
But if there is no text allowing it, then by default, it can only be a card you control, ie, something on your side of the field.
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Yes, you can attack with the Tribute Summoned monster unless a card effect tells it not to or it is after the Battle Phase.
Yes, of course you can. You can tribute it for the cost of an effect, or in main phase 2, for a Tribute Summon.
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.
Summoner of Illusions states "Tribute 1 other monster". It cannot tribute itself for its own effect.
As Destiny Hero - Plasma's equip effect is a "Once Per Turn" effect, yes it can, and the existing monster is destroyed.