The giant impact phase of terrestrial planet formation establishes connections between super-Earths orbital properties (semimajor axis spacings, eccentricities, mutual inclinations) and interior compositions (the presence or absence of gaseous envelopes). Using N-body simulations and analytic arguments, we show that spacings derive not only from eccentricities, but also from inclinations. Flatter systems attain tighter spacings, a consequence of an eccentricity equilibrium between gravitational scatterings, which increase eccentricities, and mergers, which damp them. Dynamical friction by residual disk gas plays a critical role in regulating mergers and in damping inclinations and eccentricities. Systems with moderate gas damping and high solid surface density spawn gas-enveloped super-Earths with tight spacings, small eccentricities, and small inclinations. Systems in which super-Earths coagulate without as much ambient gas, in disks with low solid surface density, produce rocky planets with wider spacings, larger eccentricities, and larger mutual inclinations. A combination of both populations can reproduce the observed distributions of spacings, period ratios, transiting planet multiplicities, and transit duration ratios exhibited by Kepler super-Earths. The two populations, both formed in situ, also help to explain observed trends of eccentricity vs. planet size, and bulk density vs. method of mass measurement (radial velocities vs. transit timing variations). Simplifications made in this study --- including the limited timespan of the simulations, and the approximate treatments of gas dynamical friction and gas depletion history --- should be improved upon in future work to enable a detailed quantitative comparison to the observations.
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