Is /etc/sudoers file only suppose to have read only permissions?
Solution 1:
Yes, /etc/sudoers is supposed to have those permissions, being read-only for user and group, nothing else. The reason being that you aren't supposed to edit the sudoers file directly, but by using the visudo wrapper, which provides some sanity checking before writing a new sudoers file.
You can control what editor visudo uses by setting the VISUAL alt. EDITOR environment variable.
$ sudo EDITOR=emacs visudo