  Dynamical correlations of various local operators are studied in the
spin-half two-channel Kondo (2CK) model in the presence of channel anisotropy
or external magnetic field. A conformal field theory-based scaling approach is
used to predict the analytic properties of various spectral functions in the
vicinity of the two-channel Kondo fixed point. These analytical results compare
well with highly accurate density matrix numerical renormalization group
results. The universal cross-over functions interpolating between
channel-anisotropy or magnetic field-induced Fermi liquid regimes and the
two-channel Kondo, non-Fermi liquid regimes are determined numerically. The
boundaries of the real 2CK scaling regime are found to be rather restricted,
and to depend both on the type of the perturbation and on the specific operator
whose correlation function is studied. In a small magnetic field, a universal
resonance is observed in the local fermion's spectral function. The dominant
superconducting instability appears in the composite superconducting channel.
