I used to have a few when I was younger, they can climb(I lost 2 before I figured out how they could get out. I thought my sister kept letting them out, but caught one climbing the corner of the tank just after the 2nd one got out. Both the escapees died.
Mine always just ate crickets and bloodworms, but I don't know if that was good enough(they did last quite a few years though), but I was a kid and didn't pay much attention to the important stuff. If they were alive, back then, that was good enough for me. There are probably a ton of caresheets out there though.
As for telling them apart, I think just the males have a call. I can't remember how accurate that info was(whether or not
just the males call), but it sounds like a fainting honking noise if I recall.