Can I voluntarily divulge things about myself that HR is not allowed to ask me?

The reason they aren't allowed to ask you certain questions is that they are not allowed to consider the answers to those questions when making employment decisions. By providing privileged information to them, you are implying that either you don't know anything about employment law, or that, although you know about it, you think they might be willing to break the law if you give them the information they need to do it. Neither one reflects positively on you.