Free-Electron Lasers (FELs) with ultra-intense coherent beams have been widely used for a variety of research, such as interrogations of the inner structure of atoms, molecules, clusters, and tightly-spaced crystal structures. Unfortunately, X-ray light sources suffer from both a high cost and limited scientific beam time, due to their kilometer-scale accelerator. On the other hand, laser-plasma accelerators (LPAs), enabling the production of high-quality MeV to GeV electron beams, are compact, less expensive, and have the electron and secondary radiation beams synchronized with a femtosecond laser driver. Here we pursue the technology required for a compact LPA based FEL, which has the capability to deliver high intensity coherent radiation pulses. A state-of-the-art 100-TW-class laser system dedicated to demonstrating an LPA based FEL was constructed. As part of this system, a novel online, non-destructive laser diagnostic, capable of measuring the transverse position and pointing angle of the laser at focus was developed. The diagnostic is based on a unique double-surface-coated wedged-mirror design for the final steering optic in the laser beamline. It produces a witness beam highly correlated with the main beam. By propagating low-power kHz pulses to the focus, the spectra of the focal position and pointing angle fluctuations with their dominant frequencies below 70 Hz, were observed. This diagnostic was also used to characterize the excellent position and pointing angle correlation of the 1-Hz high-power laser pulses to this low-power kHz pulse train, opening a promising path to implementing fast non-perturbative feedback concepts, even on few-Hz-class high-power laser systems. Furthermore, new aspects of the design and physics of an LPA based FEL, which are unique to the electron beam generated by the LPA, were investigated. One method to achieve coherent radiation in an FEL driven by an LPA is to reduce the electron beam slice energy spread by stretching the beam in a chicane, producing a linear energy chirp. Seed radiation at the resonant wavelength propagating in an undulator with the energy chirped beam may then be coherently amplified. With such a linear-energy-chirped beam, it is observed in simulations using GENESIS that the peak frequency of the seeded FEL radiation redshifts linearly with the amount of electron beam chirp and the undulator propagation distance, and inversely with the undulator wavelength and electron energy. This observed FEL radiation redshifting is explained by the dispersion of the microbunching structures during propagation due to the energy chirp of the electron beam, and analyzed using the coupled Maxwell-Vlasov equations describing the FEL dynamics.