The lack of young splicers are simply because shooting kids would bump up the game’s rating too high. There are no doubt children still running around Rapture, but we just don’t meet them. Splicers are deranged but still have some sense about them, so no doubt they keep their kids back home.
Big Sisters aren’t really female Big Daddy’s. Big Daddy’s are brainwashed, mutated men specifically created to protect the Little Sisters. It’s an entire process. Big Sisters are simply Little Sisters who grew up. ADAM slugs, for some reason, produce the most ADAM inside adolescent girls. So when those girls grow up they stop being useful as ADAM factories but they retain the enhancements, so they are “repurposed” into Big Sisters.