Yes. When you declare the attack, you, as the turn player, gets first chance to respond to it. Your opponent can respond too, either in chain to your card, or starting a new chain himself if you don't.
After this chain resolves though, or both players confirm they don't want to respond, a new chain can still be started, the turn does not immediately proceed to the Damage Step.
This chain is not 'in response' to the attack, the timing for that was passed when both players said they did not want to respond. You could activate Skill Drain here, and while the opponent can still chain cards to it, it is not the response window for the attack declaration, cards like Sakuretsu Armor cannot be activated now.
No. Negate Attack targets an opponent's monster, it cannot be used on one you control.
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, 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.
Firstly, it's an important distinction to know that players have Priority, monsters do not. Priority is a player's right to activate something. Sometimes Priority can be restricted, depending on the last game action. For example, the turn player has Priority at the start of the main phase, and after a successful summon, and after the opponent activates something. However in each case, what he can do with his Priority, is different. After a summon, the turn player has Priority. He had it before, and still has it after. With this Priority, he can do one of the following things - activate an Ignition Effect (of any one of his monsters, not just the summoned one)or activate a Spell Speed 2 card or effect. (Left out Spell Speed 3 because there aren't any spell speed 3 effects that could be activated at this time). Next thing to consider are Triggers. Triggers will 'take up' the turn player's Priority and automatically place themselves at chain link 1. If multiple things were triggered, they form a chain with each other. Lastly, it also means an opponent's trigger can place itself as chain link 1, denying the turn player a chance to put an Ignition Effect there. So when you successfully summon Barbaros, his trigger will activate and place itself as chain link 1. The opponent can chain things to this, but as usual, destroying or removing Barbaros from the field, will not prevent his effect from resolving.
Yes, that's totally fine. Traps can be activated in your opponent's turn, including continuous ones.
Since DD Sprite can only be summoned during your own turn, its trigger will activate in the opponent's Standby Phase.
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.
If either you or your opponent does not have any cards in the Hand, Hand Destruction may not be activated as you cannot fulfill its requirements needed to activate. To be able to activate Hand Destruction, you AND your opponent must have at least 2 cards each.Also, even if you legally activate it, you and your opponent must still have at least 2 cards in hand when Hand Destruction resolves, or else it will resolve without effect. Such a situation could occur if Hand Destruction was activated, and something was chained that would make one player have less than two cards in hand.