Parallax shifts the direction of a star back and forth.
Proper motion moves the star progressively farther with time.
Once the proper motion is known, one can remove it from the parallax measurements done over a year. The emission and absorption lines correspond to exactly the same changes in atomic energy levels. One would need to completely ionize the atoms of the thin gas, in order to eliminate the absorption line spectrum. The surface temperature of a star determines the level of ionization of the gas as well as the manner in which the atomic energy levels in the constituent atoms and ions are populated. Higher temperatures cause higher levels of ionization and result in the atoms and ions of the gas being in higher energy levels and vice versus for lower surface temperatures.