Hi Maurus,
Indeed, the open_basedir restriction is entirely up to your host. You can contact them and ask that they allow execution from the path above web-root.
Another option to test is moving your templates out of /system/expressionengine/
If you are saving template-as-files, your template directory can be anywhere you like. It needs to be on the same server, writable and available via file path. You can move your templates back under web-root while keeping system above for security.
Can you try that and let me know the results?
Also, let me know if that raises more questions than it answers!
Cheers,