Yes, it is possible to write on a file in the onboard SD card. Actually the datalogger example does that, it is located under the SD examples. Regarding the error you are getting it seems your IDE is loading the SD library from other version of IDE. I’d suggest you to re-install the Arduino IDE 1.5.3 in a different location where you have installed another Arduino IDE. Also keep in mind that other Arduino IDE versions store libraries and sketches under Documents/Arduino as well as the 1.5.3, so you can try changing the name to that folder to see if he is importing libraries from other IDE. Please try this and let me know if it works.
Thank you JPMontero_Intel, the compiling is successful after I rename the original library folder which is use by Arduino
thank you so much