The one that you use when gyarados has like 10 hp left and is asleep. I caught it witha regular pokeball...
I caught it with a regular pokeball but u can use an ultra ball but i wouldn't use my master ball.
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Darkrai can be caught in any kind of Poke Ball, but Ultra Ball has 4x the catch rate by itself, which is pretty high.
Yes, you can catch Dialga without a Master Ball. Dialga can be caught with any kind of Poké Ball but Dusk Balls and Ultra Balls would be the better options.
You don't need to do anything. Just enter the code. When you throw any kind of Poke Ball, it will be like a Master Ball, even if the Pokemon is at full health.
If you're talking about what kind of balls are the best to use, I'd recommend Dusk Balls if you're fighting at night, since they have a 3.5 x catch rate. But if you know that it's going to take a long time to catch Ho-Oh, then I would use a Timer Ball, which is amazing if you're going to be battling it for at least 30 turns.
if you want my opinion, Gyardos is way better. It is a better battler than Milotic. However, Milotics usually have higher HP, but that kind of depends on the level you compare them at.