We present optical HST STIS observations made with two slits crossing four of the optically brightest starburst clumps near the nucleus of M82. These provide Hα kinematics, extinction, electron density, and emission measures. From the radial velocity curves derived from both slits we confirm the presence of a stellar bar. We derive a new model for the orientation of the bar and disk with respect to the main starburst clumps and the cluster M82-A1. We 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 farther out from the nucleus but heavily obscured. We derive extremely high interstellar densities of 500-900 cm-3, corresponding to ISM pressures of P/k ≈ (0.5-1.0) × 107 cm-3 K, and discuss the implications of the measured gas properties 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 signal-to-noise ratios 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-1) underlying component to the bright Hα line and discuss the physical mechanism(s) that could be responsible for such widths. We conclude that evaporation and/or ablation of material from interstellar gas clouds caused by the impact of high-energy photons and fast flowing cluster winds produce a highly turbulent layer on the surface of the clouds from which the emission arises.