The LIGO/Virgo collaboration has detected gravitational waves from dozens of binary black hole mergers. Accurate determination of the source parameters of these binaries is important for understanding the environments in which these objects can form and merge. Many techniques are employed to speed up the parameter estimation of events in LIGO/Virgo data. We demonstrate the success of the machine learning technique of normalizing flows for inferring the parameters of several LIGO events in a matter of milliseconds, and validate the novel machine learning pipeline against the widely used technique of parallel-tempered MCMC. Orbital eccentricity of a compact binary object is a signature of dynamical formation in dense stellar clusters. We employ two novel waveform models to investigate the effects of eccentricity on the detection and parameter estimation of the gravitational wave signal. We find that, for LIGO-type detectors, the signal-to-noise ratio (SNR) of eccentric signals is larger than that of quasi-circular mergers for e < 0.4. Furthermore, for future detectors such as Einstein telescope, the SNR of eccentric signals is similar to that of quasi-circular signals, and can still have appreciable SNR up to e < 0.6. We then investigate the effect of using quasi-circular waveforms for the parameter estimation of eccentric signals. We find that for eccentrities up to e_0 < 0.3, there is an up to 10% overestimation of the system's chirp mass, and the recovered mass ratio is determined to be closer to unity regardless of the true mass ratio. We also employ a full inspiral-merger-ringdown waveform to perform parameter estimation of two gravitational wave events, GW151226, and GW170608. We find that the chirp mass and eccentricity measurements are also correlated in real data, and furthermore that there is a correlation of the chirp mass and spin that can lead to spurious eccentricity measurements in the case of a signal with appreciable spin. We measure the eccentricities of these two events and constrain them to be < 0.15 and < 0.12 for GW151226 and GW170608 respectively.