Hello again, just a short update / a workaround, which is not really ideal, but at least it works: for testing I attached an USB to serial converter to one of the USB-ports of the fox, tested the communication using the then available serial port /dev/ttyUSB0, and to my surpise there the "0x00"-byte is as well received as also sent. So I tested my program using this port, and this also works fine, which means that I can communicate with the serial device using this port.
Due to the fact that I did not change anything in my original implementation, and also still use the same version of the Java KVM as before to communicate with the serial port, I'm pretty sure that it is really a problem when using (at least) /dev/ttyS0. I just also tried it with another foxboard with another OS image (an older foxboard "classic" 4-16), and this behaves the the same way: ttyS0 does not "like" a 0x00 byte, but on ttyUSB0 it works fine. But this really only is a workaround; I'd really prefer to use one of the on-board serial ports. So if someone has another idea what to try with ttyS0 - I'd be thankful for any hints... ;-)
