We present a sample of 341 "little red dots" (LRDs) spanning the redshift range z similar to 2-11 using data from the CEERS, PRIMER, JADES, UNCOVER, and NGDEEP surveys. 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 enables the detection of LRDs over a wider redshift range and with less 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 similar to 4.5, which may tie the emergence of these sources to the inside-out growth that galaxies experience during this epoch. We find that LRDs are similar to 1 dex more numerous than X-ray- and UV-selected active galactic nuclei (AGN) at z similar to 5-7. Within our sample, we have identified the first two X-ray-detected LRDs. An X-ray spectral analysis confirms that these AGN are moderately obscured with log(N-H/cm(2)) of 23.3(-1.3)(+0.4) and 22.72(-0.16)(+0.13). 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 observations from the RUBIES survey 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 blueshifted 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.