Example of an extproc.ora File in Oracle

It looks like the hardening was a little to hard. Oracle does need some access to the server. You can revert back the chmods for ping, Oracle rdbms does not need it. /tmp/ is not required, a usable location for tmp is, mostly for scripting. The rdbms has it's own tricks and storage for sorts.

Never install Oracle as root; use the root.sh at the end of the installation to do the system tweeks required. On some platforms there is a root pre script that should run before installation. The Oracle installation scripts refuse to run using the root account and can be run using any other account.

The access to some server config files has been made a little too tight for the install user to check the prerequisites. If you know they are ok, it's ok. Proving they are ok is a little easier when support issues arise. Check the group ownership of the critical config files and add the Oracle installation user to that group to give it read access.

Simplified with window functions:

with hier as
    (select   level as the_level, <columns>
      from <tables>
        start with <predicate>
        connect by prior <child> = <parent>
    ), levels as
    (select hier.*, count(*) over (order by the_level) as count_items
      from hier
    )
  select levels.*
    from levels
    where the_level = count_items ;