Our goals are to generate narrow-band Terahertz (THz) waves and high brilliance quasi-monochromatic X-rays using about a 30-40 MeV electron beam. The experiments are planned at the FAST (Fermi Accelerator Science and Technology) facility. The low energy beamline consists mainly of a photocathode, an RF gun, two L-band superconducting accelerating cavities, a chicane and a beam dump. To generate THz waves, we use micro-bunched beams to be produced using a slit-mask installed in the middle of the chicane. Also, the electron beam is decompressed with cavity phases set off-crest for clear longitudinal separation of the micro-bunches. In 2017, we carried out experiments with 30 MeV electron beams and detected signals of the micro-bunching using a skew quadrupole magnet in the chicane and a pyrometer. The details of micro-bunch beam production, the detection of THz radiation and comparison with simulations are discussed. As for X-rays, during a short experimental run in 2016 we tried to create high brightness X-rays using electron channeling in a single diamond crystal. We present the simulated X-ray spectrum including the background bremsstrahlung contribution, and optimization of the relevant electron-beam parameters required to maximize the X-ray brilliance. The average brilliance in our experiment is expected to be about one order of magnitude higher than that in previous experiments.