I have scanned the forum and have managed to turn off the RSS and Post icons in the header in Atahualpa, but still have the links.
How can I remove all the RSS and Post links in the header above the search box?

Did you set RSS Settings -> Show Post Feed icon? / Show Comment Feed icon? to "No"?

To each his own but I'm really curious as to why in God's name would you want to remove the RSS?

RSS is what makes a blog outperform a conventional website in Google.

A conventional website garners a single entry in Google
A blog generates a half dozen or more entries for each post.

This amounts to a 6 to 1 ratio (or better if you maximize the benefits of RSS)

Why would you want to disavow yourself of this powerful capital?

the ROI on a blog is unbelievably huge relative to the ROI from a conventional website