  We study the equation of state at finite temperature and density in
two-flavor QCD with the RG-improved gluon action and the clover-improved Wilson
quark action on a $ 16^3 \times 4$ lattice. Along the lines of constant physics
at $m_{\rm PS}/m_{\rm V} = 0.65$ and 0.80, we compute the second and forth
derivatives of the grand canonical partition function with respect to the quark
chemical potential $\mu_q = (\mu_u+\mu_d)/2$ and the isospin chemical potential
$\mu_I = (\mu_u-\mu_d)/2$ at vanishing chemical potentials, and study the
behaviors of thermodynamic quantities at finite $\mu_q$ using these derivatives
for the case $\mu_I=0$. In particular, we study density fluctuations at
none-zero temperature and density by calculating the quark number and isospin
susceptibilities and their derivatives with respect to $\mu_q$. To suppress
statistical fluctuations, we also examine new techniques applicable at low
densities. We find a large enhancement in the fluctuation of quark number when
the density increased near the pseudo-critical temperature, suggesting a
critical point at finite $\mu_q$ terminating the first order transition line
between hadronic and quark gluon plasma phases. This result agrees with the
previous results using staggered-type quark actions qualitatively. Furthermore,
we study heavy-quark free energies and Debye screening masses at finite density
by measuring the first and second derivatives of these quantities for various
color channels of heavy quark-quark and quark-anti-quark pairs. The results
suggest that, to the leading order of $\mu_q$, the interaction between two
quarks becomes stronger at finite densities, while that between quark and
anti-quark becomes weaker.
