It depends on what the effect actually 'is'.
If the effect specifically responds to another action, like a negation effect, then it is a Quick Effect and can be activated at (almost) any time during your turn, and again during the opponent's turn.
If it waits for something to happen and then automatically does something, then it is a Trigger, which is spell speed 1 but will activate at any time, when the condition is met. So it can activate at almost any point in your turn, and again, in the opponent's too.
If the effect specifically says that it can be used in the opponent's turn, this by default is a spell speed 2 ability and can be activated at almost any time in either turn.
But finally if the effect has none of the above, then it is just a regular Ignition Effect which can only be activated in your own Main Phases. Being 'once per turn' alone does not tell you what type of effect it is, or when it can be used. Once per turn Ignition Effects are actually 'once per YOUR turn', and cannot be used in the opponent's turn either.
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.
It lasts every end phase.
No, you can't.
Yes, as long as it is Spell Speed 2 or 3, and Set on the field previously in the case of a Quickplay Spell or Trap card. That means the opponent can potentially do something before you get your first opportunity to activate a spell speed 1 card or perform a summon.
Yes, of course. Trap Cards can be activated in the End Phase.
Standby phase is in a yugioh duel after draw phase,you could use card effect at standby phase.
Yes, of course. Exactly the same as main phase 1.
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.
It lasts every end phase.
Yes, Stardust Dragon can activate its negation Quick Effect in the Battle Phase, and even the Damage Step.
No, you can't.
Odin says that if he is destroyed, you may resummon him by removing a Tuner from your graveyard, during that turn's End Phase, ie, the turn in which he was destroyed. If you have no Tuners that turn, then you can't activate this effect, and if you pass that turn's End Phase, then you have passed the time to activate it, so it does not matter to Odin if you get a Tuner in your graveyard after that.
Yes, as long as it is Spell Speed 2 or 3, and Set on the field previously in the case of a Quickplay Spell or Trap card. That means the opponent can potentially do something before you get your first opportunity to activate a spell speed 1 card or perform a summon.
Yes, of course. Trap Cards can be activated in the End Phase.
Yes. To be used in the battle phase, it must be a Quick Effect, and if it's a Quick Effect then it can be used in either players' turn.
If you know about the card Judgment Dragon, it's pretty much the same thing. You can activate its effect as many times as you want during your Main Phase 1 or 2 to blow up the field except itself.
Since DD Sprite can only be summoned during your own turn, its trigger will activate in the opponent's Standby Phase.