Assuming you are talking of the movie, the answer lies in the prior movie, The Rise of Darkrai. The battle between Dialga and Palkia in that movie caused massive damege to the Reverse World, enraging Giratina. Wanting revenge, Giratina tried to kill Dialga.
it is because in the movie that palkia and dialga battle the distortion world became with alot of toxic clouds, so giratina wanted revenge with palkia and dialga.
source: I watched both movies
No, Giratina doesn't want to. It is possible that he does what to because he wants space EVERYWHERE.
No one really knows, it's the way game freak wanted it, also Giratina was also banished for his violence, and he's being violent so, that could be another thing. In the end no one really knows the answer to that question, also doesn't that make it entertaining.