SMFForum integration?....

First check your hosting.
1) in php.ini set
memory_limit=16M ; better 24M
or for php5
memory_limit = 128M ; Maximum amount of memory a script may consume (128MB)
or in .htaccess
php_value memory_limit 24M
but some hostings not allow this
ask your provider about memory_limit you have
2) disable core forum module and all not needed for test purposes modules
Blog API
Contact
Poll
Search
Statistics

but enable path.module and enable clean URLs if possible

You may temporally rename or remove file smf_api_2.php to login and restore it later.

Clear out your cookies and try again.

Just installed the SMF, but not able to connect to the database! Don't know much about this forum. Do I need to install the actual SFM application from simplemachines.org? Will there be two different databases running on my Server in order to successfully integrate SFM with Drupal?

Yes, you need 2 databases. One for Drupal, one for SMF.

Thanks! I appreciate your help!...

This readme.txt file doesn't make any sense to someone who doesn't know anything about this forum and module. I am logged in the SMFForum and Drupal and I still have the message:

"You are not authenticated in SMF now. Please login to SMF and test again. You may refresh settings!"

and the solution in the readme assumes you know everything about SMF and Drupal and doesn't break it down step by step...

as said:

If you see message "You are not authenticated in SMF now." beenig logged in SMF and Drupal
as admin, it is probably mean your settings are wrong.

You should go to SMF settings and revise Server and qookie settings or do something else
in your environment, site and forum layout and settings.

8) Ensure that SMF profile fields map with corresponding
drupal profile.module fields.

9) Ensure that corresponding profile.module fields exist.
If necessary create profile.module fields that will be match with
SMF profile fields.

......what are you talking about?