The best place to start is Considerations for New Header Fields in RFC7230; it covers most common questions, and has a checklist for header authors.
If you have questions, the best place to ask is the HTTP Working Group mailing list.
New HTTP headers ought to be registered, to assure that you don’t collide with other headers, and so that people can more easily find out more about your header when they see it. RFC3864 explains how.
New HTTP methods are relatively uncommon, because a lot of the value in HTTP is having a constrained, generic set of methods.
Considerations for New Methods in RFC7231 is a good place to start for those thinking about creating a method.
If your idea for a new method seems like a good idea after reading that, the best thing to do is to bring it up on the HTTP Working Group mailing list.
Like methods, new HTTP status codes are fairly rare – not least because there are only a limited number of unused codes available.
Considerations for New Status Codes in RFC7231 is a good place to start for those thinking about creating a status code.
If you have an idea for a new status code, the best thing to do is to bring it up on the HTTP Working Group mailing list, where people can discuss it and point you in the right direction if this isn’t the best solution for your problem.