Hello again,
I fixed the empty log-file. Here are the updated patches.

The problem was this line:
>+                        "--nodaemonize" "-p" "/var" "--fpm-config"

When --nodaemonize is set, the log is printed to stdout instead.
I also removed -p "/var". It is not required when the log, pid and
socket locations are defined in the config.
Both were caused, because I didn't use pid-files from the start.

Happy Hacking!