None of the errors in log have anything to do with FA. They are possibly from LiveProjects.
Since you are using Linux Mint 17.1 which is the equivalent of Ubuntu 14.04 (Trusty Tahr) which in turn is based on Debian 8.0 (jessie), you will not be using PHP v5.3.x for which FA 2.3 has been designed. It is also possible that your .htaccess file (which is for Apache 2.2) may be invalid for Apache 2.4 you are using. Remove the .htaccess file temporarily and see if it works. MySQLi driver is being used in these later versions of PHP instead of MySQL - you will need FA v2.4.x for use with MySQLi or backport them.
State your PHP / MySQL / Apache versions and what is in your FA_webroot/tmp/error.log file.
Ubuntu <=> Debian equivalents:
15.04 vivid jessie
14.10 utopic jessie
14.04 trusty jessie
13.10 saucy wheezy
13.04 raring wheezy
12.10 quantal wheezy
12.04 precise wheezy
11.10 oneiric wheezy
11.04 natty squeeze
10.10 maverick squeeze
10.04 lucid squeeze