While I had figured out what the problem was, not being able to read "PHP" prevented me from seeing the solution staring me right in the face.

The issue was that I did not understand that the syntax dirname(__FILE__). represented the relative path for the running script.  As TM mentioned,

  This was why my entries were all being evaluated relative to the includes directory, even when I thought I was entering an absolute path.

I have now set it to be

which will give me the expected WEBROOT/tmp location, and is also "portable" if I were to move my installation to another folder/directory.

Thanks again to all who responded with suggestions.

Hope the explanation helps anyone else who may stumble on this issue as I did.  Now, on to evaluate FA on its merits.

Before the installation wizard
After decompressing the files to the frontaccounting installation folder, run the following commands:
(change /var/www/html/frontaccounting to your FrontAccounting installation path)

sudo chown -R www-data:www-data /var/www/html/frontaccounting

Then run the installation wizard and get yourself setup

After the installation wizard, run the following, to revoke user www-data write access to the config files

sudo chown root:root /var/www/html/frontaccounting/config.php
sudo chown root:root /var/www/html/frontaccounting/config_db.php

Typical config.php modifications after installation:
-timezone
-show users online
-login max 3 times (brute force prevention)

Check security on the diagnostics link in FrontAccounting to confirm it is good to go.

may be the parent or folder, which doesnot have the access to work on.

You can either use an absolute path:
ini_set('session.save_path', '/opt/FrontAccounting/tmp/');

or append the relative path to the current directory:
ini_set('session.save_path', dirname(__FILE__).'/../tmp/');

I recommend the latter, as it does not make any assumption about where FA is actually installed.

I set the session.save_path setting as directed in the  includes/session.inc file.  However, I am seeing various errors, which suggests that there is a problem with parsing the path as set in the file.

1.  If I use ini_set('session.save_path', dirname(__FILE__).'/tmp/'); - that is setting the path to /tmp, then I get the following errors:

Unknown: Failed to write session data (files). Please verify that the current setting of session.save_path is correct (/opt/FrontAccounting/includes/tmp/)

2. if If I use ini_set('session.save_path', dirname(__FILE__).'./tmp/'); - that is setting the relative tmp path to /opt/FrontAccounting/tmp, then I get the following errors:

Failed to write session data (files). Please verify that the current setting of session.save_path is correct (/opt/FrontAccounting/includes./tmp/)

3. if If I use ini_set('session.save_path', dirname(__FILE__).'/opt/FrontAccounting/tmp/'); - that is explicitly setting the path to /opt/FrontAccounting/tmp, then I get the following errors:

 Unknown: Failed to write session data (files). Please verify that the current setting of session.save_path is correct (/opt/FrontAccounting/includes/opt/FrontAccounting/tmp/)

It looks like the path is being read as relative to ./includes and not from the Dir_Root (/opt/FrontAccounting). 
If I make a symlink in ./included pointing to /opt, thereby making the paths valid, then everything seems to work (so far).  However, i don't know what else would end up breaking with this workaround, so I would prefer not to have to use it.

Eventually managed to get everything setup, and can login.  However, having an issue.
After clicking on any link, I'm returned to the login screen.  If I login, then I get to that previously clicked page, but I have to login after every click.

On the page(s), I get 4 lines of  errors:

session_start(): open(/opt/FrontAccounting/includes/opt/FrontAccounting/tmp//sess_hpsp7onb2fq9l0a05p85ts8in5, O_RDWR) failed: No such file or directory (2) in file: /opt/FrontAccounting/includes/session.inc at line 29
session_write_close(): open(/opt/FrontAccounting/includes/opt/FrontAccounting/tmp//sess_k7f4dqh3h1k89mnh9r8i189cj2, O_RDWR) failed: No such file or directory (2) in file: /opt/FrontAccounting/includes/session.inc at line 86
session_write_close(): Failed to write session data (files). Please verify that the current setting of session.save_path is correct (/opt/FrontAccounting/includes/opt/FrontAccounting/tmp/) in file: /opt/FrontAccounting/includes/session.inc at line 86
session_start(): open(/opt/FrontAccounting/includes/opt/FrontAccounting/tmp//sess_k7f4dqh3h1k89mnh9r8i189cj2, O_RDWR) failed: No such file or directory (2) in file: /opt/FrontAccounting/includes/session.inc at line 90

The application is installed at /opt/FrontAccounting, which is the webroot for the V-host.  Apparently, the script is picking up the directory as a relative path as opposed to an absolute, and thus, is duplicating it, as in "/opt/FrontAccounting/includes/opt/FrontAccounting/tmp//". Note that there is also a double slash at the end of the path.

I have checked the permissions and they seem to be OK.

Any pointers?