Did you just completely ignore the suggestion to look at self hosting communities? This is one of the most popular things ever for people to self host. There's plenty of info out there on this.

Yes, you absolutely can run your own DNS resolver on your own hardware, and many people do. It's a hell of a lot easier than running an email server. There are a whole bunch of different projects and tools to do so, with different feature sets.

I'd recommend starting with PiHole, which is an ad blocking service that runs as a DNS server you can self host. It supports running a reverse DNS service underneath it rather than passing any non-blocked requests out to a third party DNS server.