Of course, a Master Ball catches any Pokemon without fail, Legendary or not.
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you get a master ball from proffeser rowen to catch Dialga
A Master Ball
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.
there is no master ball in diamond and also great ball. but there is silver ball-silver ball is like a master ball.
Darkrai can be caught in any kind of Poke Ball, but Ultra Ball has 4x the catch rate by itself, which is pretty high.