Only if the card's effect specifically says you can, then yes, such as monsters affected by Soul Exchange, or Chimeratech Fortress Dragon.
At all other times, a tribute must be something you control. Dogma does not say you can use the opponent's monsters, so you must use your own.
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It all depends on the tokens being used. They can be used to Tribute Summon unless said otherwise on the card. For example, the card "Scapegoat" says: "...The tokens [summoned by this card] cannot be used as a Tribute for a Tribute Summon."Take note of this last condition (a Tribute for a Tribute Summon). That means the tokens can be tributed for a Special Summon for monsters such as "Destiny Hero - Plasma".Tokens that can be used for a Tribute Summon include: "Stray Lambs", "Statue of the Wicked", "Fiend's Sanctuary", and "Dandylion".
Not quite. A Synchro Summon is a Special Summon. A Tribute Summon is the same as a Normal Summon, except that when you Tribute Summon you need to tribute monsters. Also you can Special Summon as many times as you want to in a turn, whereas you can only Normal Summon OR Tribute Summon once per turn, except with a card effect.
Yes, monsters may be 'tribute set'.
No, your opponent cannot Normal or Special Summon any more monsters. They can, however, Tribute Summon monsters if they will end up having fewer or an equal amount of monsters as you. In this scenario, your opponent couldn't Tribute Summon a Level 5 or 6 monster because they would still have one more monster than you. But he/ she can tributed both monsters for a Level 7 or higher monster since they would end up with one monster. The same rule applies to tributes for a Special Summon for cards like "Destiny Hero - Plasma", "Voltanis the Adjudicator", Destiny Hero - Dogma", and more.
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.