We report on high-resolution X-ray spectroscopy of the ultracompact X-ray binary pulsar 4U 1626-67 with Chandra/HETGS acquired in 2010, two years after the pulsar experienced a torque reversal. The well-known strong Ne and O emission lines with Keplerian profiles are shown to arise at the inner edge of the magnetically-channeled accretion disk. We exclude a photoionization model for these lines based on the absence of sharp radiative recombination continua. Instead, we show that the lines arise from a collisional plasma in the inner-disk atmosphere, with $Tsimeq 10^7$ K and $n_e sim 10^{17}$ cm^(-3). We suggest that the lines are powered by X-ray heating of the optically-thick disk inner edge at normal incidence. Comparison of the line profiles in HETGS observations from 2000, 2003, and 2010 show that the inner disk radius decreased by a factor of two after the pulsar went from spin-down to spin-up, as predicted by magnetic accretion torque theory. The inner disk is well inside the corotation radius during spin-up, and slightly beyond the corotation radius during spin-down. Based on the disk radius and accretion torque measured during steady spin-up, the pulsars X-ray luminosity is $2times 10^{36}$ erg/s, yielding a source distance of 3.5(+0.2-0.3) kpc. The mass accretion rate is an order of magnitude larger than expected from gravitational radiation reaction, possibly due to X-ray heating of the donor. The line profiles also indicate a binary inclination of 39(+20-10) degrees, consistent with a 0.02 Msun donor star. Our emission measure analysis favors a He white dwarf or a highly-evolved H-poor main sequence remnant for the donor star, rather than a C-O or O-Ne white dwarf. The measured Ne/O ratio is 0.46+-0.14 by number. In an appendix, we show how to express the emission measure of a H-depleted collisional plasma without reference to a H number density.
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