I know nothing about puns in those languages because my vocabulary is limited to about a couple of dozen words in Hindi and practically none in any other Indian language except my own. My language is a young one natively spoken by about a quarter of a million people. We do puns but, like you said, English is perhaps *the* language that's wide open to puns.
Ever read the Asterix series of comic books? I sometimes wondered how they could retain the puns without losing them in the translation to English.