Then I thought it would also be possible to program the XBee with the serial monitor (but when I type +++, I don't get 'OK')
Why do you want to do this? It's far easier to put the XBee on the USB Explorer and program it that way.
Which shield? The one from Sparkfun?
I find it easiest to have two USB Explorers, and get the XBees talking to each other before worrying about connecting them to the Arduino. Once I know the XBees talk, getting data from the Arduino to the PC, via the XBees, has never been a problem.