Yes. Right after you defeat Galactic Boss Cyrus once. I recommend you don't use it on Palkia, though, as there are much harder legendary Pokemon after the game. Use it on Mesprit or Cresselia later on.
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yes palkia is a legendary thank you you need a a master ball to catch palkia
Yes, a master ball always works on any pokemon any time.
CYou can cacth Palkia in ultra ball or master ball.
When you come to meet Palkia or Dialga at MT.Corenet
you should use it on a very hard legendary Pokemon like dialga palkia giratina shaymin or arceus