We perform a detailed forecast on how well a Euclid-like survey will be able to constrain dark energy and neutrino parameters from a combination of its cosmic shear power spectrum, galaxy power spectrum, and cluster mass function measurements. We find that the combination of these three probes vastly improves the survey's potential to measure the time evolution of dark energy. In terms of a dark energy figure-of-merit defined as (sigma(w_0) sigma(w_a))^-1, we find a value of 454 for Euclid-like data combined with Planck-like measurements of the cosmic microwave background (CMB) anisotropies in a fiducial LambdaCDM cosmology, a number that is quite conservative compared with existing estimates because of our choice of model parameter space and analysis method, but still represents a factor of 3 to 8 improvement over using either CMB+galaxy clustering+cosmic shear data, or CMB+cluster mass function alone. We consider also the survey's potential to measure dark energy perturbations in models wherein the dark energy is parameterised as a fluid with a nonstandard non-adiabatic sound speed, and find that in an optimistic scenario in which w_0 deviates by as much as is currently observationally allowed from -1, models with c_s^2 = 10^-6 and c_s^2 = 1 can be distinguished at more than 2sigma significance. Under the same optimistic assumptions, if the Jeans mass associated with dark energy clustering falls within the cluster mass range observed by the survey, then the order of magnitude of the dark energy sound speed can potentially be pinned down. Finally, we find that the sum of neutrino masses can be measured with a 1sigma precision of 0.01eV, even in complex cosmological models in which the dark energy equation of state varies with time. (abridged)We perform a detailed forecast on how well a {\sc Euclid}-like survey will be able to constrain dark energy and neutrino parameters from a combination of its cosmic shear power spectrum, galaxy power spectrum, and cluster mass function measurements. We find that the combination of these three probes vastly improves the survey's potential to measure the time evolution of dark energy. In terms of a dark energy figure-of-merit defined as $(\sigma(w_{\mathrm p}) \sigma(w_a))^{-1}$, we find a value of 690 for {\sc Euclid}-like data combined with {\sc Planck}-like measurements of the cosmic microwave background (CMB) anisotropies in a 10-dimensional cosmological parameter space, assuming a $\Lambda$CDM fiducial cosmology. For the more commonly used 7-parameter model, we find a figure-of-merit of 1900 for the same data combination. We consider also the survey's potential to measure dark energy perturbations in models wherein the dark energy is parameterised as a fluid with a nonstandard non-adiabatic sound speed, and find that in an \emph{optimistic} scenario in which $w_0$ deviates by as much as is currently observationally allowed from $-1$, models with $\hat{c}_\mathrm{s}^2 = 10^{-6}$ and $\hat{c}_\mathrm{s}^2 = 1$ can be distinguished at more than $2\sigma$ significance. We emphasise that constraints on the dark energy sound speed from cluster measurements are strongly dependent on the modelling of the cluster mass function; significantly weaker sensitivities ensue if we modify our model to include fewer features of nonlinear dark energy clustering. Finally, we find that the sum of neutrino masses can be measured with a $1 \sigma$ precision of 0.015~eV, (abridged

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