Full-duplex (FD) integrated sensing and communication (ISAC) has great potential in future vehicular networks. However, the FD requirement and the ISAC functions make the receiver processing extremely complicated, particularly when multiple transmissions are uncoordinated. In this paper, we study frequency-hopping (FH) based receivers in an FD ISAC system, where the arrivals of backscattered signals from one node may overlap with those of signals from another node. To mitigate the interferences caused by the overlapping signals, we consider two receiver options based on either conventional communications or frequency-modulated continuous-wave radars, and two signal modulations based on either fast FH or un-slotted ALOHA FH. Based on the different signal modulations, we develop two parameter estimation schemes via using FH-decoding and de-chirp operations, respectively. To further improve the sensing accuracy, we proceed to propose an iterative algorithm, which refines the estimates of all parameters via using short-time-Fourier transform and maximizing the received power in desired frequency bands. After obtaining all channel parameters in sensing, bilateral communications between two nodes are realized by differential phase-shift keying. Finally, simulation results are provided and verify that the proposed FD ISAC can obtain parameters in high resolution and realize robust communication links.