Yes, You can catch Groudon in Pokemon Emerald.
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No you can only get groudon in Pokemon ruby or emerald and transfer through Pal Park or if you have heart gold or silver soul you can catch and trade groudon to yourself
you can`t catch kyogre or groudon or both of them without linking them from sapphire, ruby or emerald version.
you can use master ball in caught the groudon
You can catch any Pokemon with any ball it all depends on luck.
you cannot get groudon in emerald