  We present an interstellar medium and stellar population analysis of three
spectroscopically confirmed $z>7$ galaxies in the ERO JWST NIRCam and JWST
NIRSpec data of the SMACS J0723.3-7327 cluster. We use the Bayesian spectral
energy distribution (SED) fitting code \texttt{Prospector} with a flexible
star-formation history (SFH), a variable dust attenuation law, and a
self-consistent model of nebular emission (continuum and emission lines).
Importantly, we self-consistently fit both the emission line fluxes from JWST
NIRSpec and the broad-band photometry from JWST NIRCam, taking into account
slit-loss effects. We find that these three $z=7.6-8.5$ galaxies
($M_{\star}\approx10^{8}~M_{\odot}$) are young with rising SFHs and
mass-weighted ages of $3-4$ Myr, though we find indications for underlying
older stellar populations. The inferred gas-phase metallicities broadly agree
with the direct metallicity estimates from the auroral lines. The galaxy with
the lowest gas-phase metallicity ($\mathrm{Z}_{\rm
gas}=0.06~\mathrm{Z}_{\odot}$) has a steeply rising SFH, is very compact
($<0.2~\mathrm{kpc}$) and has a high star-formation rate surface density
($\Sigma_{\rm
SFR}\approx22~\mathrm{M}_{\odot}~\mathrm{yr}^{-1}~\mathrm{kpc}^{-2}$),
consistent with rapid gas accretion. The two other objects with higher
gas-phase metallicity show more complex multi-component morphologies on kpc
scales, indicating that their recent increase in star-formation rate is driven
by mergers or internal, gravitational instabilities. We discuss effects of
assuming different SFH priors or only fitting the photometric data. Our
analysis highlights the strength and importance of combining JWST imaging and
spectroscopy for fully assessing the nature of galaxies at the earliest epochs.
