How do I make a file NOT modifiable?

You can set the "immutable" attribute with most filesystems in Linux.

chattr +i foo/bar

To remove the immutable attribute, you use - instead of +:

chattr -i foo/bar

To see the current attributes for a file, you can use lsattr:

lsattr foo/bar

The chattr(1) manpage provides a description of all the available attributes. Here is the description for i:

   A  file with the `i' attribute cannot be modified: it cannot be deleted
   or renamed, no link can be created to this file  and  no  data  can  be
   written  to  the  file.  Only the superuser or a process possessing the
   CAP_LINUX_IMMUTABLE capability can set or clear this attribute.