DFT of 2d real signal and Hermitian symmetry
Yes, multidimensional DFT's have complex conjugate symmetry in each dimension 

I think you might be misinterpreting the FFTW manual which is referring to internal storage formats.

Edit:


  why the transformed vector in FFTW is diminished only by half (only
  one dimension values are stored on N/2+1 complex numbers)? Why isn't
  each direction diminished?


From the FFTW manual:


  The multi-dimensional transforms of FFTW [...] compute simply the separable product of the given 1d transform along each dimension of the array 


So for example if you provide a 256x256 array of real numbers the result will be 256 1 dimensional DFT's. As they mention at the bottom of that documentation this is not a multi-dimensional DFT.

see http://www.fftw.org/fftw3_doc/Complex-Multi_002dDimensional-DFTs.html