This is the second part of our study of the properties and limitations of nonlinearity-induced nonreciprocal devices. In the first part, we discussed the general working principle of nonreciprocal devices based on resonators filled with Kerr-like nonlinearities, and we showed that strong nonreciprocal responses can be obtained when an asymmetric resonator is excited from only one port with a quasi-monochromatic signal. In this second part, we further investigate their behavior under more complex input signals. Specifically, we discuss simultaneous two-port excitations, which are expected to be detrimental to isolation purposes due to the lack of linearity of these devices. We show, however, that this regime can be used to achieve novel functionalities, such as optically controlled transmission switching. In order to assess the device performance in realistic scenarios, we also investigate how noise and random inputs affect the nonreciprocal response. Finally, we show how increasing the system complexity can help to overcome some device limitations, and lead to novel applications such as bandpass nonreciprocal filters. Overall, this work shows that nonlinearity-induced nonreciprocal devices, with their appealing passive, bias-free operation, offer interesting opportunities for various practical application scenarios and may form the basis for a plethora of new technologies of great relevance for microwave engineering systems, from radars and lidars to classical and quantum signal processing and computing.