Where is the include of stddef.h? Because there NULL is defined.
A short test with the Arduino IDE shows that at least the following
are included automagically by the IDE before compilation.
at the photo you can see the first lines of main that i have included some of the .h and that after compiling the problems still exist. I have opened project properties to see that i have included the folder /lib in the directories of the c and c++ compiler and i though that i could do the same with this INCLUDE "folder" that does not appear as you see by yourself inside the project.
If an include folder would not have been accepted by the IDE, you would get errors from the compiler about not found header files. As you told us that you don't get such error messages it seems that all include files you specified are really found by the compiler. Or have you forgotten to tell us about such error messages?