Is the speaker impedance constant or variable?

It differs with the frequency that is being produced, and its usually toward the lowend on the scale that you see a sharp drop in the ohmage from norm. There are others out there that can explain it better than I, but I do know there is very little constant about ohmage, and usually if you look into the fine print of a speaker you will see that the ohmage is given as an average, which means it is not constant.

Impedance will vary by frequency response.
Each model of any speaker will have a different impedance curve. This is based on the different drivers in the speaker (maybe crossover too??).

Speaker impedance IS reactive, and varies according to frequency. The original WATT speakers were notoriously difficult to drive due to a HUGE impedance dip in the lower registers ... not as much a problem when used with a sub and active Xover, avoiding those frequencies. For excellent discussions of this and other technical issues find "The Audio Amateur" and "Amateur Speaker Builder" periodicals online. There are also plenty of speaker design books that will explain the technicalities in a fashion I can't.