  We study a system describing the compressible barotropic fluids interacting
with (visco) elastic solid shell/plate. In particular, the elastic structure is
part of the moving boundary of the fluid, and the Navier-slip type boundary
condition is taken into account. Depending on the reference geometry (flat or
not), we show the existence of weak solutions to the coupled system provided
the adiabatic exponent satisfies $\gamma > \frac{12}{7}$ without damping and
$\gamma > \frac{3}{2}$ with structure damping, utilizing the domain extension
and regularization approximation. Moreover, via a modified relative entropy
method in time-dependent domains, we prove the weak-strong uniqueness property
of weak solutions. Finally, we give a rigorous justification of the
incompressible inviscid limit of the compressible fluid-structure interaction
problem with a flat reference geometry, in the regime of low Mach number, high
Reynolds number, and well-prepared initial data. As a byproduct, by low Mach
number we also derive the incompressible limit with reduced assumptions on the
regularity of the structure but with a stronger assumption on the exponent of
$\gamma$.
