Image rescaling requires GD2 lib.
TeraWURFL plugin requires bzip2 lib to be installed and PHP5 with mysqli to work (MySQL5 is highly recommended). The rights for procedure creation and execution in MySQL5 are highly recommended.
Also TeraWURFL required about 25Mb of space in database. The tables contain information about almost all mobile devices in the world (screen resolution, markup language, etc), and the size cannot be reduced (actually there is a way to install MobileJoomla without TeraWURFL, see below).
In the case of own server it is sufficient to have PHP5, gd2 and bzip libraries, working mysqli, and MySQL5 with rights for procedure creation.
In most cases it means that your server is limited in resources and Joomla has no time/memory to unpack MobileJoomla archive (check your error_log for info about the error). Try to unpack it to Joomla’s tmp directory and do install from the directory.
Also there is a way to unpack MobileJoomla archive, remove /plugins/terawurfl directory, pack it back to new archive, and install such a “limited” version of MobileJoomla. In this case you will get working MobileJoomla, but without TeraWURFL plugin.
Most likely it means that PHP was compiled without mysqli support, or mysqli lib is not installed (that is mysqli class is not defined in PHP). Also check that mysqli.so (php_mysqli.dll in Windows) extension is loaded in php.ini.
The problem is that MobileJoomla cannot unzip tera_dump.sql.bz2 file. Workaround here is to unpack tera_dump.sql.bz2 to the root of your site or to download http://www.mobilejoomla.com/tera_dump_095.sql and put it to the root of site (where configuration.php is placed) as tera_dump.sql. Then reinstall MobileJoomla. The MobileJoomla installation procedure will use this file in the case of problems with unpacking original bzip2-file.
It maybe because php is run in CGI/FastCGI mode with very short timeout (it is not related to max_execution_time in php.ini) that doesn’t allow MobileJoomla installer to finish install procedure.
During install MobileJoomla tries to unpack tera_dump.sql.bz2 file. If it is impossible on your server (that is either bz2 php extension is not loaded or bunzip2 program is not installed) then MobileJoomla tries to download unpacked version (~20Mb) from mobilejoomla.com. Most likely you have a problem with downloading tera_dump.sql (that is php is able to open connection with remote server, but cannot download any data, or downloading speed is very low). So, as a solution it is recommended to install/enable bz2 php-extension.
Choose mysql4 mode in “Mobile-TeraWURFL” plugin settings.
Most likely you assigned mobile_*** template to a menu item. Note that mobile templates in MobileJoomla are not usual templates. They may be loaded through “Mobile Joomla Plugin” plugin only (and not as usual templates). That is why you cannot assign them to menu items or view them in preview mode. If you would like to give users a link to mobile version, do it with MobileJoomla’s MarkupChooser module.
iphonetester.com doesn’t change “user agent string”, and it is not an actual emulator as it uses your browser to load and render page. Try to use Firefox browser with UserAgentSwitcher extension to work with iphonetester.com. The typical “User Agent String” of iPhone is “Mozilla/5.0 (iPhone; U; CPU like Mac OS X; en) AppleWebKit/420+ (KHTML, like Gecko) Version/3.0 Mobile/1A543a Safari/419.3” (without quotes).
Check that all the menu items are correctly translated in JoomFish as default language of mobile device may differ from the language of desktop browser.