no
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Arceus has a catch rate of 3, so you need LOTS of Ultra Balls. If you have a Master Ball, you can easily catch it. He is ridiculous, because it takes so long to catch him! I recommend master balls!
Of course, a Master Ball catches any Pokemon without fail, Legendary or not.
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.
Any Pokémon is catchable without the Master Ball, though some-especially Legendaries-are harder than others.
No, this is completely impossible. A Master Ball cannot fail at capturing Pokemon, so it will capture any Pokemon, even Arceus.