My sketches so far have been very simple, and I have been able to tell if they were performing correctly by reading what was sent by the Fio over XBee to the PC. Anyway, my point is that I did not use a dedicated debugging tool.
I get it now, that Serial.write writes to the serial port. And I am able to read that data in the Serial Monitor. Great! However, that data is also sent on the XBee radio. I set up the radio as they suggest here: http://arduino.cc/en/Main/ArduinoBoardFioProgramming. Can I set up the XBee module such that I can write to the XBee radio and not to the serial port (the six physical pins on the Fio) and vice versa? I think if I can achieve that, then I am ready to go.
Side note: I am researching the battery behaviour (safety mechanisms agains over-draining and over-charging), charging behavior, voltage measurement etc. I will get back about this when I know a bit more. Thanks for the hints.