  We present the results of a high-resolution imaging survey of 22 brown dwarfs
and very low mass stars in the nearby (~145 pc) young (~1-2 Myr) low-density
star-forming region Taurus-Auriga. We obtained images with the Advanced Camera
for Surveys/High Resolution Channel on HST through the F555W (V), F775W (i'),
and F850LP (z') filters. This survey confirmed the binarity of MHO-Tau-8 and
discovered a new candidate binary system, V410-Xray3, resulting in a binary
fraction of 9+/-5% at separations >4 AU. Both binary systems are tight (<10 AU)
and they possess mass ratios of 0.75 and 0.46, respectively. The binary
frequency and separations are consistent with low-mass binary properties in the
field, but the mass ratio of V410-Xray3 is among the lowest known. We find that
the binary frequency is higher for very low mass stars and high-mass brown
dwarfs than for lower-mass brown dwarfs, implying either a decline in frequency
or a shift to smaller separations for the lowest mass binaries. Combining these
results with multiplicity statistics for higher-mass Taurus members suggests a
gradual decline in binary frequency and separation toward low masses. The
implication is that the distinct binary properties of very low-mass systems are
set during formation and that the formation process is similar to the process
which creates higher-mass stellar binaries, but occurs on a smaller scale. We
show that there are no planets or very low-mass brown dwarfs with mass >3 M_J
at projected separation >40 AU orbiting any of the Taurus members in our
sample. We identify several BDs with significant (>1 mag) V-band excesses. The
excesses appear to be correlated with signatures of accretion, and if
attributed to accretion luminosity, may imply mass accretion rates several
orders of magnitude above those inferred from line-profile analyses. (abridged)
