Transport properties of NbN/NiCu superconductor/ferromagnet (S/F) nanostripes fabricated in both in single-wire and series-parallel, meander-type configurations are presented down to T = 4.2 K. In particular, the enhancement of the superconducting critical current has been observed at smaller widths, apparently, due to an extra pinning mechanism, arising from clustering of ferromagnetic atoms inside the thin S layer. Moreover, we observed a number of characteristic voltage steps on the nanostripe current-voltage characteristics and their nature was investigated as a function of temperature. An explanation in terms of active phase-slip phenomena has been proposed based of the time-dependent Ginzburg-Landau theory and led to an estimation of the inelastic electron-phonon relaxation time τe-ph ~ 1 ps, in agreement with the τopt = 1.2±0.3 ps value, measured by the femtosecond transient optical reflectivity spectroscopy method on the same bilayer. Transient optical properties of our superconducting S/F nano-bilayers have been also investigated and compared to those obtained for pure NbN nanostripe reference samples. Finally, electrical photoresponse signals of S/F heterostructures exposed to ultraweak pulsed (width 400 ps, repetition rate ~100 MHz) laser radiation at 850 nm wavelength exhibited the falling time of voltage responses directly dependent on the NiCu overlayer. We have also noticed that the presence of the top F layer and the resulting proximity effect reduced frequency of dark counts in our samples.