  We present a study of the individual super star clusters (SSCs) in the
low-metallicity galaxy SBS 0335-052 using new near-infrared and archival
optical Hubble Space Telescope observations. The physical properties of the
SSCs are derived from fitting model spectral energy distributions (SEDs) to the
optical photometry, as well as from the H_alpha and Pa_alpha nebular emission.
Among the clusters, we find a significant age spread that is correlated with
position in the galaxy, suggesting successive cluster formation occurred in SBS
0335-052 triggered by a large-scale disturbance traveling through the galaxy at
a speed of ~35 km/s. The SSCs exhibit I-band (~0.8 um) and near-IR (~1.6-2.1
um) excesses with respect to model SEDs fit to the optical data. We hypothesize
that the I-band excess is dominated by a photoluminescent process known as
Extended Red Emission; however, this mechanism cannot account for the excesses
observed at longer near-IR wavelengths. From the cluster SEDs and colors, we
find that the primary origin of the near-IR excess observed in the youngest
SSCs (<3 Myr) is hot dust emission, while evolved red supergiants dominate the
near-IR light in the older (>7 Myr) clusters. We also find evidence for a
porous and clumpy interstellar medium (ISM) surrounding the youngest, embedded
SSCs: the ionized gas emission underpredicts the expected ionizing luminosities
from the optical stellar continuum, suggesting ionizing photons are leaking out
of the immediate vicinity of the clusters before ionizing hydrogen. The
corrected, intrinsic ionizing luminosities of the two SSCs younger than ~3 Myr
are each ~ 5x10^52 s^-1, which is equivalent to each cluster hosting ~5000 O7.5
V stars. The inferred masses of these SSCs are ~10^6 M_sun.
