Is there any possibility to modify for example a specific GPIO status, or shutdown the Raspberry Pi or modify crontab on it from a website which is run on another web server?
The IP-Address of the Raspberry Pi2 is static and I can normally ping the website from it.
Thanks in advance
modify for example a specific GPIO status
pigpio is a library for the Pi doing just that. Using a daemon and socket interface it is possible to controll GPIO pins on a remote system. Simple examples are provided on the linked page.
shutdown the Raspberry Pi or modify crontab
This has probably been answered a few times before.