  K2 photometry is suitable for the exploitation of mode variability on short
timescales in hot B subdwarf stars, which is important to constrain nonlinear
quantities addressed by the stellar theory of high-order perturbation in the
future. We analyze the $\sim80$~d high-quality K2 data collected on PG~0101+039
and extract the frequency content of oscillation. We then determine its
rotational and orbital properties, as well as characterize the dynamics of
amplitude and frequency. The frequencies are extracted from light curves via a
standard prewhitening technique. The binary information is obtained from
variations both in brightness and radial velocities. Amplitude and frequency
modulation of oscillation modes are measured by piece-wise light curves and
characterized by EMCMC method. We have extracted 137 independent frequencies in
PG~0101+039 and derived period spacing of ~252s and 144s for the dipole and
quadruple modes, respectively. We derive a rotation rate of 8.81+-0.06d and
~8.60+-0.16d based on g- and p-mode multiplets, implying a marginally
differential rotation with a probability of ~ 60%. We find that the rotation
period is much shorter than the orbital period of ~0.57d, indicating that this
system is not synchronized. Amplitude and frequency modulation are measurable
for 44 frequencies with high enough amplitude, including 12 rotational
components. We characterize their modulating patterns and find a clear
correlation between amplitude and frequency variation, which is linked to
nonlinear resonant couplings. In general, the modulating scale and timescale
are on an order of a few dozen of nano hertz and a few tens of days,
respectively, whose values are important constraints to future calculations of
nonlinear amplitude equations.
