The Kirchhoff-law-Johnson-noise (KLJN) system is a classical physical secure key exchange scheme based on the Kirchhoff's circuit loop law and the fluctuation-dissipation theorem of statistical physics. This dissertation contains two main studies related to this scheme: bit error analysis and removal, and applications in vehicular communication systems. The thesis starts with a presentation of some of the challenges faced by modern communications. It also includes a description of the working principle of the KLJN system and the motivation upon which this dissertation is built. Then, a study of the errors in this scheme is carried out. In the first part, the types of errors due to statistical inaccuracies in the voltage-based and current-based measurement modes are classified and analyzed. In both measurement modes and for all types of errors, at fixed bandwidth, the error probabilities decay exponentially versus the duration of the bit sharing period. In the second part, an error removal method is proposed to improve the fidelity of the system. This method is based on the combination of the voltage-based and current-based schemes and it drastically reduces the error probabilities. The second topic of study in the thesis explores a potential practical application for the KLJN key exchange scheme. First, we present a vehicular communication network architecture with unconditionally secure KLJN keys. Secondly, a new solution for secure KLJN key donation to vehicles is proposed and an upper limit for the lifetime of this key is given. A summary of the work is given in the last section and the main results of the research are discussed. These contributions include: closed-form expressions for the error probabilities in the KLJN system, error removal methods without the need of implementing any error correcting technique, and a new potential vehicular application for the KLJN scheme. Some of the future research initiatives related to these topics are discussed.