I am a survivor of abuse, perpetrated by another child, my brother.
For me 13 is too young. WAY too young. 16...maybe, but 17 or 18 would be a more realistic minimum for me.
Male vs. female....i'd need to know the teenager AND his/her family to call that one. My friend's son is 15 and i can imagine at 17 or so i would trust him to look after 5+yo kids. My DD rarely needs help with the toilet and if she did i know he would assist her with mild distaste and get it over with as quick as possible. But i know him, and i know his folks/family and their dynamic. His mum is a MW (was MY MW) and he's used to the female form in all its various forms, i wouldn't be concerned that he would see a butt and think "oh my i gotta investigate" when wiping down my 5yo. There is a woman, a grown woman, in my family i would never leave my kids with, because she is toxic. I don't think she would sexually molest specifically, but i wouldn't put any kind of abuse past her. I do not trust her, she feels "icky" to me in my gut. Our neighbour's DD is 18 or 19 and i would leave DD with her in a heartbeat. I know her family, i know her, she's responsible and kind, DD loves her, there would be no worries for me. If i had to pick between my friends DS and my neighbours DD i'd chose my neighbours DD, but that's mainly because MY DD would want to play dolls, put on nail varnish and sparkles and play dancing and i think my neighbours DD would enjoy that more than the friend's DS.
A lot can be said about abuse and risk assessment and so on. I think EVERYONE should read Protecting The Gift. And beyond that you need to know who the people you're leaving kids with are, where they come from (family dynamics) and above all, be willing to reassess them at any stage. Most abuse occurs because a parent considers someone once, decides they're ok, and then refuses to re-examine that opinion even in the face of quite scary information. For example my parents decided our headmaster of the elementary school was a fine babysitter. They decided when they found a 16-year-old foreign exchange student who was staying with that man hysterically sobbing in his home and begging them not to tell anyone that "he must be gay then and they've had a tiff" (WTF? He was SIXTEEN and hundreds of miles from his home and family!) and continued to leave us there. My brother was another victim of this man and i was a victim of my brother. People will go to incredible lengths to avoid looking at the ugly thing right in front of their faces. It is no good, really, assuming that every teenage boy might molest, when what you need to do is ADMIT when you suspect a good, loved, wonderful teenage boy you thought you knew is doing so.