I have old version of minibb...so I want to update into new version...anyone has idea to help me?

Read The Manual First!

You might check this thread as well:

Upgrade and Upgrading / Migrating guides

Specially pay attention at post #2.

If you are having difficulties yourself, don't forget that we are providing paid support for upgrades.

I cannot find the UPDATE.txt file in the downloaded 2.5 version, do we need this?
QUOTE from manual:
"When you are ready to upgrade, download latest miniBB release, and start checking !UPDATE.txt file from the version you currently have."

!UPDATE.txt is not located in the core miniBB distribution, but in Updates history package. It's also available online.

I want to upgrade to the latest MiniBB version which I believe is 3.1.1.
I currently show $version='2.0.2'; in the bb_functions.php file.
Am I to assume (Since I have read everything on upgrading and it is still unclear) that I must update from 2.0.2 to each version in between (almost 30 versions!) until I finally arrive at update to 3.1.1? Or, can I just upgrade directly from 2.0.2 to 3.1.1? If not, even wipe out the directory and start fresh with 3.1.1 (Backing up my Database for sure) ?

The most easiest moment for your case is upgrading core files - probably, you will need just to overwrite all bb_*.php files, index.php and setup_mysqli.php (or you may stay with the setup_mysql.php). The same affects all add-ons, if you have them, you need to re-install all add-ons one by one manually. Then you shold follow upgrading history file and manually update database, CSS and templates - this will be the most hard work involved. You may also hire us, if you want this job completed quickly and with no big pain for you.

Thank you Paul. I will send you a request for quote privately. You are the best!