  [abridged] We describe the results of our multi-wavelength observing campaign
on the young stellar objects in the LkH$\alpha$101 cluster. Our simultaneous
X-ray and multi-frequency radio observations are unique in providing
simultaneous constraints on short-timescale variability at both wavelengths as
well as constraints on the thermal or nonthermal nature of radio emission from
young stars. Focussing in on radio-emitting objects and the multi-wavelength
data obtained for them, we find that multi-frequency radio data indicate
nonthermal emission even in objects with infrared evidence for disks. We find
radio variability on timescales of decades, days and hours. About half of the
objects with X-ray and radio detections were variable at X-ray wavelengths,
despite lacking large-scale flares or large variations. Variability appears to
be a bigger factor affecting radio emission than X-ray emission. A star with
infrared evidence for a disk, [BW88]~3, was observed in the decay phase of a
radio flare. In this object and another ([BW88]~1), we find an inverse
correlation between radio flux and spectral index which contrasts with behavior
seen in the Sun and active stars. We interpret this behavior as the
repopulation of the hardest energy electrons due to particle acceleration. A
radio and X-ray source lacking an infrared counterpart, [BW88]~1, may be near
the substellar limit; its radio properties are similar to other cluster
members, but its much higher radio to X-ray luminosity ratio is reminiscent of
behavior in nearby very low mass stars/brown dwarfs. We find no correspondence
between signatures of particle acceleration and those of plasma heating, both
time-averaged and time-variable. The lack of correlated temporal variability in
multi-wavelength behavior, the breakdown of multi-wavelength correlations of...
