HST/STIS spectroscopy of the environment in the starburst core of M82

[Abridged] We present high-resolution optical HST/STIS observations made with two slits crossing four of the brightest starburst clumps in the vicinity of the nucleus of M82. These provide H_alpha kinematics, extinction, electron density and emission measures. From the radial velocity curves we confirm the presence of a stellar bar, and find that the super star cluster M82-A1 has a position and radial velocity consistent with it being at the end of one of the unique x2 bar orbits formed by an inner Lindblad resonance. We derive a new model for the orientation of the bar and disc with respect to the main starburst clumps, and propose that clump A has formed within the bar region as a result of gas interactions between the bar orbits, whereas region C lies at the edge of the bar and regions D and E are located further out from the nucleus but heavily obscured. We derive extremely high interstellar densities, corresponding to ISM pressures of P/k ~ 0.5-1.0 x 10^7 cm^-3 K, and discuss the implications of the measured gas properties surrounding the nuclear star clusters on the production and evolution of the galactic wind. Despite varying pressures, the ionization parameter is uniform down to parsec-scales, and we discuss why this might be so. Where the S/N of our spectra are high enough, we identify multiple emission-line components. Through detailed Gaussian line-fitting, we identify a ubiquitous broad (200-300 km/s) underlying component to the bright H_alpha line, and discuss the physical mechanism(s) that could be responsible for such widths. We conclude that the evaporation and/or ablation of material from interstellar gas clouds caused by the impact of the high-energy photons and fast-flowing cluster winds produces a highly turbulent layer on the surface of the clouds from which the emission arises.