  We present a photometric study of the dwarf galaxy population in the core
region ($< r_{\rm vir}/4$) of the Fornax galaxy cluster based on deep $u'g'i'$
photometry from the Next Generation Fornax Cluster Survey. All imaging data
were obtained with the Dark Energy Camera mounted on the 4-meter Blanco
telescope at the Cerro-Tololo Interamerican Observatory. We identify 258 dwarf
galaxy candidates with luminosities $-17 < M_{g'} < -8$ mag, corresponding to
typical stellar masses of $9.5\gtrsim \log{\cal M}_{\star}/M_\odot \gtrsim
5.5$, reaching $\sim\!3$ mag deeper in point-source luminosity and $\sim\!4$
mag deeper in surface-brightness sensitivity compared to the classic Fornax
Cluster Catalog. Morphological analysis shows that surface-brightness profiles
are well represented by single-component S\'ersic models with average S\'ersic
indices of $\langle n\rangle_{u',g',i'}=(0.78-0.83) \pm 0.02$, and average
effective radii of $\langle r_e\rangle_{u',g',i'}\!=(0.67-0.70) \pm 0.02$ kpc.
Color-magnitude relations indicate a flattening of the galaxy red sequence at
faint galaxy luminosities, similar to the one recently discovered in the Virgo
cluster. A comparison with population synthesis models and the galaxy
mass-metallicity relation reveals that the average faint dwarf galaxy is likely
older than ~5 Gyr. We study galaxy scaling relations between stellar mass,
effective radius, and stellar mass surface density over a stellar mass range
covering six orders of magnitude. We find that over the sampled stellar mass
range several distinct mechanisms of galaxy mass assembly can be identified: i)
dwarf galaxies assemble mass inside the half-mass radius up to $\log{\cal
M}_{\star}$ ~8.0, ii) isometric mass assembly in the range $8.0 < \log{\cal
M}_{\star}/M_\odot < 10.5$, and iii) massive galaxies assemble stellar mass
predominantly in their halos at $\log{\cal M}_{\star}$ ~10.5 and above.
