  We present an experimental study of density and order fluctuations in the
vicinity of the solid-liquid-like transition that occurs in a vibrated
quasi-two-dimensional granular system. The two-dimensional projected static and
dynamic correlation functions are studied. We show that density fluctuations,
characterized through the structure factor, increase in size and intensity as
the transition is approached, but they do not change significantly at the
transition itself. The dense, metastable clusters, which present square
symmetry, also increase their local order in the vicinity of the transition.
This is characterized through the bond-orientational order parameter $Q_4$,
which in Fourier space obeys an Ornstein-Zernike behavior. Depending on filling
density and vertical height, the transition can be of first or second order
type. In the latter case, the associated correlation length $\xi_4$, relaxation
time $\tau_4$, zero $k$ limit of $Q_4$ fluctuations (static susceptibility),
the pair correlation function of $Q_4$, and the amplitude of the order
parameter obey critical power laws, with saturations due to finite size
effects. Their respective critical exponents are $\nu_{\bot} = 1$, $\nu_{||} =
2$, $\gamma = 1$, $\eta=0.67$, and $\beta=1/2$, whereas the dynamical critical
exponent $z = \nu_{||}/\nu_{\bot} = 2$. These results are consistent with model
C of dynamical critical phenomena, valid for a non-conserved critical order
parameter (bond-orientation order) coupled to a conserved field (density).
