We theoretically explore the applications of a nonlinear circuit QED system, where a charge qubit is inductively coupled to an LC resonator, in the photonic engineering and ultrastrong-coupling multiphoton quantum optics. An arbitrary Fock-state pulsed maser, where the artificial qubit plays the gain-medium role, is achieved via simply sweeping the gate-voltage bias. The resonantly pumped parametric qubit-resonator interface leads to a squeezed intraresonator field, which is utilizable for the quantum-limited microwave amplification. Moreover, upwards and downwards multiphoton quantum jumps may be observed in the driving-free steady-state system.