How do I use https (SSL) in XAMPP while using virtual hosts

SSL, of the HTTPS://url.here/ variety, is entirely handled by Apache and has nothing to do with PHP, or any of PHP’s extensions/modules, or any php.ini settings.

A typical SSL Enabled VirtualHost looks like this and contains at least these parts…

<VirtualHost *:443>
    DocumentRoot "C:/WampDeveloper/Websites/www.example.com/webroot"
    ServerName www.example.com
    ServerAlias example.com

    SSLEngine On

    SSLCertificateFile "C:/WampDeveloper/Websites/www.example.com/certs/public.crt"
    SSLCertificateKeyFile "C:/WampDeveloper/Websites/www.example.com/certs/private.key"

    <Directory "C:/WampDeveloper/Websites/www.example.com/webroot">
        Options All
        AllowOverride All
        order allow,deny
        allow from all
    </Directory>

</VirtualHost>

(The paths above are from my WampDeveloper Pro set up, Xampp’s will be slightly different)

Your <VirtualHost *> line is faulty. It needs a port number, which is always 443 for an HTTPS:// URL, in combination with either an IP address or a star before it. And if using a star, also a NameVirtualHost *:443 line…

NameVirtualHost *:80
NameVirtualHost *:443

<VirtualHost *:80>
    DocumentRoot "C:\xampp\htdocs"
    ServerName localhost
</VirtualHost>
<VirtualHost *:443>
    DocumentRoot "C:\Users\user_name\Documents\project_one"
    ServerName project_one.localhost
    SSLEngine on
    SSLCertificateFile "conf/ssl.crt/server.crt"
    SSLCertificateKeyFile "conf/ssl.key/server.key"
    <Directory "C:\Users\user_name\Documents\project_one">
        AllowOverride All
        Order allow,deny
        Allow from all
    </Directory>
</VirtualHost>
<VirtualHost *:80>
    DocumentRoot "C:\Users\user_name\Documents\project_two"
    ServerName project_two.localhost
    <Directory "C:\Users\user_name\Documents\project_two">
        AllowOverride All
        Order allow,deny
        Allow from all
    </Directory>
</VirtualHost>