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I have a set of fMRI images (.nii.gz). Now I want to infer the in-plane resolution and the slice thickness. Can this information and perhaps additional information be retrieved with FSL or Matlab? And yes, how?

Or can I calculate it somehow?

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The information you seek is contained in the header of the image file. Matlab has open source tools for reading the header information. e.g., http://www.mathworks.com/matlabcentral/fileexchange/29344-read-medical-data-3d

If you want an even more open source option, NiBabel is an open source python library for reading .nii files (header and image). I think the command print(header.get_data_shape()) will return the image dimensions. See http://nipy.org/nibabel/nibabel_images.html#the-image-header for instructions.

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