Azimuthal non-uniform propellant supply operation shows representative characteristics of suppressed discharge oscillation and increased axial electron current. These characteristics implicate that, with non-uniform operation, physics underlying oscillation and electron transport in Hall thrusters may be able to be studied in a spatiotemporally less strict experimental setup. From this insight, we investigated azimuthal plasma properties of non-uniform propellant operation and its influences on discharge oscillation and electron cross-field transport. The image analysis result reveals non-linear plasma structures elongated in direction of electron azimuthal E × B drift, showing the structure is governed by electrons. From probe measurements, inhomogeneous electron temperature distribution in azimuth direction is observed, and corresponding azimuthal inharmonic ionization is thought to partially contributes to the suppressed discharge oscillation. Also, macroscopic zeroth order azimuthal distribution of plasma potential and electron density shows the distribution is self-consistently generated in a way to enhance electron cross-field drift towards the anode. We estimated amount of current carried by equilibrium zeroth order distribution, which accounts for about 20% of total increased electron current in the non-uniform operation. The physical similarities of the macroscopic transport to microscopic instability induced electron transport are also compared.