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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.
Yes, as long as it's your own turn. If you want to activate them in the opponent's turn, you need to have Set them on the field during your own.
You can only do so in your turn. You may do so during Main Phase like a normal Spell Card. You can also do so to start a Chain. For example, if your monster attacked and your opponent activated Mirror Force, you can Chain My Body as a Shield from your hand. If you plan to activate a Quick-play Spell Card during your opponent's turn, however, you must Set your Quick-play Spell Card during your Main Phase.
yes
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, this is one of the main advantages of a Quickplay Spell. But to activate it in the opponent's turn, it must have been Set on the field in the previous turn.
In general, yes. Continuous effects are only applied while the monster is on the field, an activated effects (Ignition, Trigger and Quick) can only activate when the monster is on the field. If they activate in other zones (Honest, while in hand, Zeta Reticulant, while in the graveyard, DD Survivor, while out of play) then it will specifically say so on the card.
Nothing. Without a card in hand, Ordeal of the Traveler's effect can't activate when an attack is declared, because it is unable to resolve.
with shadow clones
During your turn, you can play a Quick-play Spell from your hand during Main Phase I or II. During your opponent's turn, you can activate it only if it is already Set on your field. Like all Spells, you play a Quick-play Spell in the Magic & Trap Card Zone. When played, its effect is activated immediately like most other card effects.
Yes. There's no requirement for a Quickplay Spell to be previously set on the field, for it to be activated at any part of your turn. You can add it to a chain in progress in any phase, from hand, as long as it's your turn.
Born, wrote plays, died. Quick enough for you?