Partial fft of multidimensional array

I have a 3D array of dimension (NX,NY,NZ) which represents a variable in physical space, let's say velocities, taken from a simulation in a 3D domain.

1) I want to Fourier-transform only the dimensions X and Z, how should I use the built-in function fft in this case? At some point I want to also get back to the physical space, but only on X, so the same question applies.

2) I read that FFTW uses only 2*N/3 points, should I specify NX and NZ as the number of retained modes or fewer?

3) When using the FFTW package, is there any issue with the coefficient in front of the integral defining the Fourier transformation? Does this package assume that my domain is 2pix2pix2pi?