Support

The PHP version warning is permanent and cannot be disabled. It's placed there to let you know that your host is using PHP 5.2 which has been end-of-life since January 2011. We will drop support for it very soon. FYI, at the time of this writing the officially supported versions of PHP are 5.3 and 5.4.

Your version very old, obsolete and vulnerable. You can continue using Akeeba Backup, but you must seriously consider upgrading to PHP 5.3 or 5.4. For what is worth, future versions of Joomla! will require PHP 5.3 to work. At this moment there is no reason whatsoever not to upgrade to PHP 5.3. All modern web software (read: anything published since mid-2011) is absolutely compatible with PHP 5.3 or even requires it. Please stop thinking about it and update your servers to PHP 5.3 today.

Regarding the other warning, it's an indication of a failed or partial update. Most likely some of your files or directories have wrong permissions and can't be updated, that's why reinstalling didn't work for you. In order to work around that, you will have to perform some manual work. Remove the following folders:
- administrator/components/com_akeeba EXCEPT the administrator/components/com_akeeba/backup directory and the administrator/components/com_akeeba/akeeba/serverkey.php file. If you remove that directory and that file you will lose your existing backups and/or settings.
- components/com_akeeba
- administrator/modules/mod_akadmin
- media/com_akeeba
- plugins/system/plg_srp
- plugins/system/plg_akeebaupdatecheck
- plugins/system/plg_aklazy
- plugins/system/plg_oneclickaction
Now you can re-install Akeeba Backup.

Please note that I have tried Akeeba Backup 3.6.2 as an update from 3.6.1 and as a clean installation on Joomla! 2.5.6 running on PHP 5.2, 5.3 and 5.4. I cannot replicate the reported issue about permissions. In the interest of collecting more information which can potentially help me establish a pattern, please tell me which host you're using.

PHP 5.3 is the only sane choice. PHP 5.2, as I said, is end of life since January 2012. TIme to get rid of it :)

PHP 5.3 has been stable for too long (almost two years). All developers have updated their software to work with PHP 5.3 by now. I have switched to PHP 5.3 since a year ago (when I was still using Joomla! 1.5) and had no issues whatsoever. My blog site is running on PHP 5.3 since February 2011, also no problem even when it was using Joomla! 1.5. Of course there are no issues with Joomla! 2.5 – it's made to work perfectly on PHP 5.3 and even the pretty much just-stable (since a couple of months ago) PHP 5.4.