Apache configuration issues

I'm trying to deploy a project that is using Zend. This project is in a subfolder of the site (site.com/projects/project-name). The site is in a VPS, to which I have root access. The server is Apache 2.4.7. I configured a VirtualHost for the project, so that it had its own root and not the root of the site. The project root was then in the public folder of it, as the Zend manual asks. I did this in the /etc/apache2/sites-available/000-default.conf file. Below, the contents of the file:

<VirtualHost *:80>
    ServerName site.com.br
    ServerAlias www.site.com.br
    DocumentRoot /var/www/html/site/
    Alias /projetos/nome-projeto/ /var/www/html/site/projetos/nome-projeto/public$

    <Directory /var/www/html/site/projetos/nome-projeto/public>
            DirectoryIndex index.php
            AllowOverride All
            Order allow,deny
            Allow from all
    </Directory>

    ServerAdmin webmaster@localhost

    ErrorLog ${APACHE_LOG_DIR}/error.log
    CustomLog ${APACHE_LOG_DIR}/access.log combined
</VirtualHost>
<VirtualHost *:80>
    ServerName site.com.br
    ServerAlias www.site.com.br

    ServerAdmin webmaster@localhost
    DocumentRoot /var/www/html/site

    ErrorLog ${APACHE_LOG_DIR}/error.log
    CustomLog ${APACHE_LOG_DIR}/access.log combined
</VirtualHost>

# vim: syntax=apache ts=4 sw=4 sts=4 sr noet

The first VirtualHost is the VirtualHost of the project. The second is the VirtualHost site. When I access site.com/projects/project-name it lists the files in the project's public folder, even having an index.php in it. And if I try to enter the index.php "manually" or get on some route that I set in Zend, such as site.com/projects/project-name/route, it gives me the 404 error.

In /etc/apache2/apache2.conf, I have some settings that might be relevant to the question:

<Directory />
    Options FollowSymLinks
    AllowOverride None
    Require all denied
</Directory>

<Directory /usr/share>
    AllowOverride None
    Require all granted
</Directory>

<Directory /var/www/html/site/>
    Options Indexes FollowSymLinks
    AllowOverride All
    Require all granted
</Directory>

<Directory /var/www/html/site/projetos/nome-projeto/public/>
    RewriteEngine On
    Options Indexes FollowSymLinks
    AllowOverride All
    Require all granted
</Directory>

In advance thank you.

Update:

You can see php.ini here: link

Update 2:

Below, apache2.conf:

# This is the main Apache server configuration file.  It contains the
# configuration directives that give the server its instructions.
# See http://httpd.apache.org/docs/2.4/ for detailed information about
# the directives and /usr/share/doc/apache2/README.Debian about Debian specific
# hints.
#
#
# Summary of how the Apache 2 configuration works in Debian:
# The Apache 2 web server configuration in Debian is quite different to
# upstream's suggested way to configure the web server. This is because Debian's
# default Apache2 installation attempts to make adding and removing modules,
# virtual hosts, and extra configuration directives as flexible as possible, in
# order to make automating the changes and administering the server as easy as
# possible.

# It is split into several files forming the configuration hierarchy outlined
# below, all located in the /etc/apache2/ directory:
#
#   /etc/apache2/
#   |-- apache2.conf
#   |   '--  ports.conf
#   |-- mods-enabled
#   |   |-- *.load
#   |   '-- *.conf
#   |-- conf-enabled
#   |   '-- *.conf
#   '-- sites-enabled
#       '-- *.conf
#
#
# * apache2.conf is the main configuration file (this file). It puts the pieces
#   together by including all remaining configuration files when starting up the
#   web server.
#
# * ports.conf is always included from the main configuration file. It is
#   supposed to determine listening ports for incoming connections which can be
#   customized anytime.
#
# * Configuration files in the mods-enabled/, conf-enabled/ and sites-enabled/
#   directories contain particular configuration snippets which manage modules,
#   global configuration fragments, or virtual host configurations,
#   respectively.
#
#   They are activated by symlinking available configuration files from their
#   respective *-available/ counterparts. These should be managed by using our
#   helpers a2enmod/a2dismod, a2ensite/a2dissite and a2enconf/a2disconf. See
#   their respective man pages for detailed information.
#
# * The binary is called apache2. Due to the use of environment variables, in
#   the default configuration, apache2 needs to be started/stopped with
#   /etc/init.d/apache2 or apache2ctl. Calling /usr/bin/apache2 directly will not
#   work with the default configuration.


# Global configuration
#

#
# ServerRoot: The top of the directory tree under which the server's
# configuration, error, and log files are kept.
#
# NOTE!  If you intend to place this on an NFS (or otherwise network)
# mounted filesystem then please read the Mutex documentation (available
# at <URL:http://httpd.apache.org/docs/2.4/mod/core.html#mutex>);
# you will save yourself a lot of trouble.
#
# Do NOT add a slash at the end of the directory path.
#
#ServerRoot "/etc/apache2"

#
# The accept serialization lock file MUST BE STORED ON A LOCAL DISK.
#
Mutex file:${APACHE_LOCK_DIR} default

#
# PidFile: The file in which the server should record its process
# identification number when it starts.
# This needs to be set in /etc/apache2/envvars
#
PidFile ${APACHE_PID_FILE}

#
# Timeout: The number of seconds before receives and sends time out.
#
Timeout 300

#
# KeepAlive: Whether or not to allow persistent connections (more than
# one request per connection). Set to "Off" to deactivate.
#
KeepAlive On

#
# MaxKeepAliveRequests: The maximum number of requests to allow
# during a persistent connection. Set to 0 to allow an unlimited amount.
# We recommend you leave this number high, for maximum performance.
#
MaxKeepAliveRequests 100

#
# KeepAliveTimeout: Number of seconds to wait for the next request from the
# same client on the same connection.
#
KeepAliveTimeout 5


# These need to be set in /etc/apache2/envvars
User ${APACHE_RUN_USER}
Group ${APACHE_RUN_GROUP}

#
# HostnameLookups: Log the names of clients or just their IP addresses
# e.g., www.apache.org (on) or 204.62.129.132 (off).
# The default is off because it'd be overall better for the net if people
# had to knowingly turn this feature on, since enabling it means that
# each client request will result in AT LEAST one lookup request to the
# nameserver.
#
HostnameLookups Off

# ErrorLog: The location of the error log file.
# If you do not specify an ErrorLog directive within a <VirtualHost>
# container, error messages relating to that virtual host will be
# logged here.  If you *do* define an error logfile for a <VirtualHost>
# container, that host's errors will be logged there and not here.
#
ErrorLog ${APACHE_LOG_DIR}/error.log

#
# LogLevel: Control the severity of messages logged to the error_log.
# Available values: trace8, ..., trace1, debug, info, notice, warn,
# error, crit, alert, emerg.
# It is also possible to configure the log level for particular modules, e.g.
# "LogLevel info ssl:warn"
#
LogLevel warn

# Include module configuration:
IncludeOptional mods-enabled/*.load
IncludeOptional mods-enabled/*.conf

# Include list of ports to listen on
Include ports.conf


# Sets the default security model of the Apache2 HTTPD server. It does
# not allow access to the root filesystem outside of /usr/share and /var/www.
# The former is used by web applications packaged in Debian,
# the latter may be used for local directories served by the web server. If
# your system is serving content from a sub-directory in /srv you must allow
# access here, or in any related virtual host.
<Directory />
    Options FollowSymLinks
    AllowOverride None
    Require all denied
</Directory>

<Directory /usr/share>
    AllowOverride None
    Require all granted
</Directory>

<Directory /var/www/html/site/>
    Options Indexes FollowSymLinks
    AllowOverride All
    Require all granted
</Directory>



<Directory /var/www/html/site/projetos/nome-projeto/public/>
    RewriteEngine On
        Options Indexes FollowSymLinks
        AllowOverride All
        Require all granted
</Directory>



#<Directory /srv/>
#   Options Indexes FollowSymLinks
#   AllowOverride None
#   Require all granted
#</Directory>




# AccessFileName: The name of the file to look for in each directory
# for additional configuration directives.  See also the AllowOverride
# directive.
#
AccessFileName .htaccess

#
# The following lines prevent .htaccess and .htpasswd files from being
# viewed by Web clients.
#
<FilesMatch "^\.ht">
    Require all denied
</FilesMatch>


#
# The following directives define some format nicknames for use with
# a CustomLog directive.
#
# These deviate from the Common Log Format definitions in that they use %O
# (the actual bytes sent including headers) instead of %b (the size of the
# requested file), because the latter makes it impossible to detect partial
# requests.
#
# Note that the use of %{X-Forwarded-For}i instead of %h is not recommended.
# Use mod_remoteip instead.
#
LogFormat "%v:%p %h %l %u %t \"%r\" %>s %O \"%{Referer}i\" \"%{User-Agent}i\"" vhost_combined
LogFormat "%h %l %u %t \"%r\" %>s %O \"%{Referer}i\" \"%{User-Agent}i\"" combined
LogFormat "%h %l %u %t \"%r\" %>s %O" common
LogFormat "%{Referer}i -> %U" referer
LogFormat "%{User-agent}i" agent

# Include of directories ignores editors' and dpkg's backup files,
# see README.Debian for details.

# Include generic snippets of statements
IncludeOptional conf-enabled/*.conf

# Include the virtual host configurations:
IncludeOptional sites-enabled/*.conf

# vim: syntax=apache ts=4 sw=4 sts=4 sr noet