Laser-Compton scattering (LCS) is a novel scheme of generating highly collimated synchrotron radiation-like X-ray and $\gamma$-rays with electron accelerators much smaller in size than synchrotrons. With potentials in radiography, radio-oncology and nuclear physics, laser-Compton light sources are being studied in many places. At Lawrence Livermore National Laboratory, an X-band based 30-MeV linear accelerator was built to be used as a source of electron beam for LCS studies. This thesis describes the characterization process and results of both the electron beam and the resulting X-rays of the LLNL LCS X-ray source. A new electron beam diagnostic using the K-edge absorption effect was developed using the machine and simulation tools originally used for the characterization, which is explained in detail. Next, medical applications of LCS X-ray sources are discussed, regarding K-edge subtraction method and nanoparticle Auger therapy in particular. Lastly, the dose simulations used for Auger therapy were also applied to simulating neutron capture therapy using Boron.