I respect your boldness to ask these questions, but I don't feel like I can adequately answer them. I wrote a 6 paragraph essay but using GPT-4 as a sensitivity reader, I don't think I can post it without some kind of miscommunication or unintentional hurt. Instead, I'll answer the questions directly by presenting non-authoritative alternate viewpoints.

1. No idea, maybe someone else knows
2. That makes sense to me; I would think there would be a strong pressure to present fake content as real to avoid getting caught but they're already in deep legal trouble anyway and I'm sure they get off to it too. It's hard to know for sure because it's so stigmatized that the data are both biased and sparse. Good luck getting anyone to volunteer that information
3. I consider pedophilia (ie the attraction) to be amoral but acting on it to be "evil", ala noncon, gore, necrophilia, etc. That's just from consistent application of my principles though, as I haven't humanized them enough to care that pedophilia itself is illegal. I don't think violent video games are quite comparable because humans normally abhor violence, so there's a degree of separation, whereas CP is inherently attractive to them. More research is needed, if we as a society care enough to research it.
4. I don't quite agree, rights are hard-won and easy-lost but we seem to gain them over time. Take trans rights to healthcare for example - first it wasn't available to anyone, then it was available to everyone (trans or not), now we have reactionary denials of those rights, and soon we'll get those rights for real, like what happened with gay rights. Also, I don't see what rights are lost in arguing for the status quo that pedophilia remain criminalized? If MAPs are any indication, I'm not sure we're ready for that tightrope, and there are at least a dozen marginalized groups I'd rather see get rights first. Unlike gay people for instance, being "in the closet" is a net societal good because there's no valid way to present that publicly without harming children or eroding their protections.