Sorry for the delay.

I can buy other domains, but how do I do that without revealing who I am? Don't I have to share my real information when I purchase and register, which then becomes public knowledge through who-is lookups and all?

There is a privacy service registrars offer. There has to be contact information (email, address etc) but they can act as the third party and provide proxies to keep the customer's real info from being visible. Yes, the third party(the domain registrar) will still have all the contact info the customer has to provide. And I suppose they can be more or less susceptible to be strong-armed into revealing it to other parties, depending on the company. But I suppose the more third party(middle men) layers you can manage to put between yourself and public visibility(if that is at all possible), the more difficult it will be to get to your info.

But if you give me some Python or Javascript, or a language I don't know but can learn, I will dig into that all day every day.

Oh yeah, the latter is the one I know a wee bit of. True, that the internet space is a different beast altogether and I understand how it can be confusing. But pointing to nameservers from domains is relatively easy for people who decide to acquire one. It is done on the Registrar's site and an example of a nameserver would be something like this: ns01.000webhost.com (for 000webhost.com).

Your particular webhost will be the ones giving you the nameserver(s) that can be pointed to; And that will find the servers which provide resources for your website. That has to be arranged with the webhost.