Is there anything known about the spatial configuration of the quarks within a proton of pion? Or are they just considered to be two or three overlapping points?
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The parton distribution functions (PDFs) are momentum distributions sorted by flavor. The Fourier transforms of them give you the position distributions.
You can get similar, though sometimes less specific (i.e. no flavor information) from the form-factors or structure functions.
See also: What is an intuitive picture of the motion of nucleons? for the same kind question about the motion of the nucleons in the nucleus.
