  (abridged) A wide-field galaxy redshift survey allows one to probe galaxy
clustering at largest spatial scales, which carries an invaluable information
on horizon-scale physics complementarily to the cosmic microwave background
(CMB). Assuming the planned survey consisting of z~1 and z~3 surveys with areas
of 2000 and 300 square degrees, respectively, we study the prospects for
probing dark energy clustering from the measured galaxy power spectrum,
assuming the dynamical properties of dark energy are specified in terms of the
equation of state and the effective sound speed c_e in the context of an
adiabatic cold dark matter dominated model. The dark energy clustering adds a
power to the galaxy power spectrum amplitude at spatial scales greater than the
sound horizon, and the enhancement is sensitive to redshift evolution of the
net dark energy density, i.e. the equation of state. We find that the galaxy
survey, when combined with Planck, can distinguish dark energy clustering from
a smooth dark energy model such as the quintessence model (c_e=1), when
c_e<0.04 (0.02) in the case of the constant equation of state w_0=-0.9 (-0.95).
An ultimate full-sky survey of z~1 galaxies allows the detection when c_e<0.08
(0.04) for w_0=0.9 (-0.95). We also investigate a degeneracy between the dark
energy clustering and the non-relativistic neutrinos implied from the neutrino
oscillation experiments, because the two effects both induce a scale-dependent
modification in the galaxy power spectrum shape at largest spatial scales
accessible from the galaxy survey. It is shown that a wider redshift coverage
can efficiently separate the two effects by utilizing the different redshift
dependences, where dark energy clustering is apparent only at low redshifts
z<1.
