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Can you swim underwater?
Literal
Submerge-[and-て] can-swim [casual-question-かい].
~かい is a casual/masculine question-ender — softer and more congenial than bare ~か, typical of an older man addressing someone younger. 泳げる is the potential form of 泳ぐ ('can swim'). The ~て form on 潜水する sequences or joins the two actions — here really 'while submerged' (concurrent state) rather than a strict 'first dive, then swim.'