  Promising applications of the anisotropic quantum Rabi model (AQRM) in broad
parameter ranges are explored, which is realized with superconducting flux
qubits simultaneously driven by two-tone time-dependent magnetic fields.
Regarding the quantum phase transitions (QPTs), with assistant of fidelity
susceptibility, we extract the scaling functions and the critical exponents,
with which the universal scaling of the cumulant ratio is captured with
rescaling of the parameters due to the anisotropy. Moreover, a fixed point of
the cumulant ratio is predicted at the critical point of the AQRM. In respect
to quantum information tasks, the generation of the macroscopic Schr\"{o}dinger
cat states and quantum controlled phase gates are investigated in the
degenerate case of the AQRM, whose performance is also investigated by
numerical calculation with practical parameters. Therefore, our results pave a
way to explore distinct features of the AQRM in circuit QED systems for QPTs,
quantum simulations and quantum information processings.
