시간이 나면 뭘 하세요?
I think the translation it would be "what do you do in your free time?" - am I right? But theres no such word as "free" in here. Its just "time". Like. Literally it would be "time-if-what you do?" Can someone help me to understand it a little better? Another way to say it maybe..

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If it's a correct sentence, 나 is probably like 나오다 or 나가다, come out or go out.  So it would mean 'when you get the time/when time appears, what do you do?', I would say.  :)