Adelynmakes,
Yes! It is definitely OK to make copies or prints of your piece. Each one does not have to be an original.
cvcrossing,
You can do whatever you'd like - send each person a different one or send the same one to everybody. Yes, postcard is fine! You can make it as decorative or as simple as you like (but should contain calligraphy).
The exchanges are an opportunity to practice, get creative, and use calligraphy doing something other than drills. Having a theme gives us a focus and helps generate creative ideas. You will see there is a wide variety of what people do.
Have fun!