  We present JWST MIRI Medium Resolution Spectrograph (MRS) observations of the
$\beta$ Pictoris system. We detect an infrared excess from the central
unresolved point source from 5 to 7.5 $\mu$m which is indicative of dust within
the inner $\sim$7 au of the system. We perform PSF subtraction on the MRS data
cubes and detect a spatially resolved dust population emitting at 5 $\mu$m.
This spatially resolved hot dust population is best explained if the dust
grains are in the small grain limit (2$\pi$a$\ll$$\lambda$). The combination of
unresolved and resolved dust at 5 $\mu$m could suggest that dust grains are
being produced in the inner few au of the system and are then radiatively
driven outwards, where the particles could accrete onto the known planets in
the system $\beta$ Pic b and c. We also report the detection of an emission
line at 6.986 $\mu$m that we attribute to be [Ar II]. We find that the [Ar II]
emission is spatially resolved with JWST and appears to be aligned with the
dust disk. Through PSF subtraction techniques, we detect $\beta$ Pic b at the
5$\sigma$ level in our MRS data cubes and present the first mid-IR spectrum of
the planet from 5 to 7 $\mu$m. The planet's spectrum is consistent with having
absorption from water vapor between 5 and 6.5 $\mu$m. We perform atmosphere
model grid fitting on spectra and photometry of $\beta$ Pic b and find that the
planet's atmosphere likely has a sub-stellar C/O ratio.
