Advances in hybrid fractional quantum Hall (FQH)-superconductor platforms pave the way for realisation of parafermionic modes. We analyse signatures of these non-abelian anyons in transport measurements across devices with Z₆ parafermions (PFs) coupled to an external electrode. Simulating the dynamics of these open systems by a stochastic quantum jump method, we show that a current readout over sufficiently long times constitutes a projective measurement of the fractional charge shared by two PFs. Interaction of these topological modes with the FQH environment, however, may cause poisoning events affecting this degree of freedom which we model by jump operators that describe incoherent coupling of PFs with FQH edge modes. We analyse how this gives rise to a characteristic three-level telegraph noise in the current, constituting a very strong signature of PFs. We discuss also other forms of poisoning and noise caused by interaction with fractional quasiparticles in the bulk of the Hall system. We conclude our work with an analysis of four-PF devices, in particular on how the PF fusion algebra can be observed in electrical transport experiments.