No, Ash will not catch Meloetta.
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Ash and friends meet Meloetta in Best Wishes episode 82 and continue to interact with it until episode 97. Meloetta also appears in the special episode Meloetta's Sparkling Recital, which was a short to air alongside the 15th Pokemon movie, Kyuurem Vs The Sword of Justice.
No.
No, not yet.
Ash fought Giovanni in the Pokémon Black and White in the episode that is currently Episode 757 according to total episodes and the current episode title for it even though it's a translated title is "Meloetta and the Underwater Temple."
Meloetta is not in the game yet but will be as a via wireless gift