Assuming that the effect of "The Fabled Unicore" is active (therefore, assuming that you and your opponent have the same number of cards in your hands), both the monster effect that was activated and Doomcaliber Knight will be destroyed.
Yes, you can activate a planeswalker ability during your opponent's turn if the ability can be activated at instant speed.
No, you cannot activate planeswalker abilities at instant speed during your opponent's turn.
You can only activate a Quickplay Spell card from your hand in your own turn. If you want to activate it in the opponent's turn, you must Set it during your own turn.
Yes, in Magic: The Gathering, you can activate creature abilities on your opponent's turn if the ability can be activated at instant speed.
Yes, it is a Continuous Trap card with a Quick Effect. You can activate the card in any phase of the opponent's turn, and you can activate the effect of the card in any phase of the opponent's turn also.
Since DD Sprite can only be summoned during your own turn, its trigger will activate in the opponent's Standby Phase.
Your opponent gets the effect.
The damage from Graverobber is applied when you activate the spell card.
no, if you read it, it says that only you can.
It doesn't actually affect a player, so no.
You can only activate Quick Effects, Traps, and Quickplay Spells in your opponent's turn, as well as some cards may Trigger automatically when conditions are met. Field Spell Cards are none of the above. You cannot activate them in your opponent's turn.
No, you can't. You can only activate a Quick-play Spell on your opponent's turn if you have Set it on a previous turn.