  We examine collective modes, stability, and BCS pairing in a
quasi-two-dimensional gas of dipolar fermions aligned by an external field. By
using the (conserving) Hartree-Fock approximation, which treats direct and
exchange interactions on an equal footing, we obtain the spectrum of
single-particle excitations and long wavelength collective modes (zero sound)
in the normal phase. It appears that exchange interactions result in strong
damping of zero sound when the tilting angle between the dipoles and the normal
to the plane of confinement is below some critical value. In particular, zero
sound cannot propagate if the dipoles are perpendicular to the plane of
confinement. At intermediate coupling we find unstable modes that can lead
either to collapse of the system or the formation of a density wave. The BCS
transition to a superfluid phase, on the other hand, occurs at arbitrarily weak
strengths of the dipole-dipole interaction, provided the tilting angle exceeds
a critical value. We determine the critical temperature of the transition
taking into account many-body effects as well as virtual transitions to higher
excited states in the confining potential, and discuss prospects of
experimental observations.
