Yes, as long as the spell card is a Quickplay Spell, and the trap card is not a Counter Trap.
So you cannot chain Monster Reborn to any trap. Nor can you chain Book of Moon to a Counter Trap, for example.
You can activate Quickplay Spell cards in your opponent's turn, if you have Set them on the field. As well as that, some of your face-up continuous and continuous-like cards may have a trigger than activates when a certain condition is met, these can activate in the opponent's turn too (Black Garden is one).
Yes, spell shattering arrow does work when your opponent activates a normal spell in Yu-Gi-Oh. The shattering arrow spell destroys all face-up spell cards of your opponent.
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.
There is no real hard limit - as long as you've got a spell card in hand, and a slot in the S/T zone for it to go, then you can activate it.
Magical hats can only be used during your opponent's battle phase. Seeing as they can't flip their monsters during their battle phase, no. However, if your opponent does activate a spell or trap card during the battle phase, you can use Magical hats and protect your monsters. Overall, yes. You can use magical hats to protect your monsters from targeting effects as long as it's during your opponent's battle phase.
No; you cannot chain two Magic Drains to one Spell Card.
You can activate Quickplay Spell cards in your opponent's turn, if you have Set them on the field. As well as that, some of your face-up continuous and continuous-like cards may have a trigger than activates when a certain condition is met, these can activate in the opponent's turn too (Black Garden is one).
Yes, spell shattering arrow does work when your opponent activates a normal spell in Yu-Gi-Oh. The shattering arrow spell destroys all face-up spell cards of your opponent.
The damage from Graverobber is applied when you activate the spell card.
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Greenkappa must be able to select two valid targets, or its effect won't even activate. In your case, there is only one valid target, so Greenkappa will not activate.
Sometimes. It is an Optional Trigger so it can miss the timing. When an opponent activates a Field Spell card, your Field Spell Card is destroyed when the opponent's resolves. Your opponent's field spell card will resolve to the field, your Geartown will be destroyed, since the destruction was the last thing to happen, Geartown will Trigger. When you activate a new Field Spell Card over your own, your original one is destroyed when the new one activates. Geartown will go to the graveyard, then your new one will resolve to the field. Geartown misses the timing. If however you Set a new Field Spell Card, this doesn't use the chain. Geartown will be destroyed as above, and will also Trigger.
Yes, if your opponent activates any Spell or Trap card, it can be chained to and countered with Dark Bribe, unless it is specifically forbidden.
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.
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.
They can definitely activate them, but you can negate them. Horus Lv8 has a Quick Effect that can negate Spell Cards. If the opponent activates a Spell Card, then you can chain this negation effect to the activation. So Horus Lv8's effect will resolve and negate the Spell Card. Unless the opponent is using a card that can't be negated (Spiritualize, for example) then yes, it will prevent him from activating any spell cards. Horus Lv8 can activate this effect in the Damage Step too, so can stop effects like Shrink if used there. However to 'activate' a Spell Card means to place it directly on the field face-up or flip it face-up from being Set. If a Spell Card like 'Clock Tower Prison' was already active, Horus Lv8 is not allowed to chain his negation effect to the trigger that adds Clock Counters to it.
There is no real hard limit - as long as you've got a spell card in hand, and a slot in the S/T zone for it to go, then you can activate it.