  We present all relevant details of our calculation of the complete
next-to-leading order (O(alpha_s^2 alpha)) QCD corrections to heavy flavor
photoproduction with longitudinally polarized point-like photons and hadrons.
In particular we provide analytical results for the virtual plus soft gluon
cross section. We carefully address the relevance of remaining theoretical
uncertainties by varying, for instance, the factorization and renormalization
scales independently. Such studies are of importance for a meaningful first
direct determination of the polarized gluon density Delta g from the total
charm production spin asymmetry by the upcoming COMPASS experiment. It is shown
that the scale uncertainty is considerably reduced in next-to-leading order,
but the dependence on the charm quark mass is sizable at fixed target energies.
Finally, we study several differential single-inclusive heavy quark
distributions and, for the polarized HERA option, the total bottom spin
asymmetry.
