  We present a sample of 341 "little red dots" (LRDs) spanning the redshift
range $z\sim2-11$ using data from the CEERS, PRIMER, JADES, UNCOVER and NGDEEP
surveys. These sources are likely heavily-reddened AGN that trace a
previously-hidden phase of dust-obscured black hole growth in the early
Universe. Unlike past use of color indices to identify LRDs, we employ
continuum slope fitting using shifting bandpasses to sample the same rest-frame
emission blueward and redward of the Balmer break. This approach allows us to
identify LRDs over a wider redshift range and is less susceptible to
contamination from galaxies with strong breaks that otherwise lack a rising red
continuum. The redshift distribution of our sample increases at $z<8$ and then
undergoes a rapid decline at $z\sim4.5$, which may tie the emergence, and
obscuration, of these sources to the inside-out growth that galaxies experience
during this epoch. We find that LRDs are 2-3 dex more numerous than bright
quasars at $z\sim5-7$, but their number density is only 0.6-1 dex higher than
X-ray and UV selected AGN at these redshifts. Within our sample, we have
identified the first X-ray detected LRDs at $z=3.1$ and $z=4.66$. An X-ray
spectral analysis confirms that these AGN are moderately obscured with
$\log\,(N_{\rm H}/{\rm cm}^{2}$) of $23.3^{+0.4}_{-1.3}$ and
$22.72^{+0.13}_{-0.16}$. Our analysis reveals that reddened AGN emission
dominates their rest-optical light, while the rest-UV originates from their
host galaxies. We also present NIRSpec follow-up spectroscopy of 17 LRDs that
show broad emission lines consistent with AGN activity. The confirmed AGN
fraction of our sample is $71\%$ for sources with F444W$<26.5$. In addition, we
find three LRDs with narrow blue-shifted Balmer absorption features in their
spectra, suggesting an outflow of high-density, low ionization gas from near
the central engine of these faint, red AGN.
