I think it would depend on how its used. Sin is used when the possessor is the same as the subject of the sentence, e.g., "She kissed her husband" meaning her own husband would use sin, but if it were someone else's husband it would be hennes. So, I think the way it would be used (please someone correct me if I'm wrong here!) would be in a sentence like "In his/her youth, he/she got into trouble a lot", but I think you'd use hennes/hans in a sentence like "I knew him in his youth"?
Yes, pretty much. I sin ungdom brukade hon spela fotboll 'In her youth, she used to play football/soccer'. The tense in your sentence must be the simple past spelade, not the past perfect that you used, because the past perfect refers to a result, and we don't have that here. I min ungdom spelade jag fotboll.
Edit: I think I sort of missed the point here at first. You should say När jag var barn… if you're speaking about your childhood. När jag var ung… is about when you were young, not when you were a child.