I have an ancient server running Red Hat 7. I would like to update the httpd set up and obviously Red Hat does not provide updates for a system this old. What would be the best method to update these services on this machine?
Honestly your best bet may be to update the OS. You're going to have to compile from source and chances are you will be compiling dependencies of the Apache and PHP from the source too.
You may have some luck getting the rpms from a source like this rpm.pbone.net