Is it normal for ink to be consumed even when I am not actively printing on the HP Deskjet 1010?

Yes, ink from the cartridges is used in several ways beyond active printing, including during the initialization process that prepares the device and cartridges for printing, and during printhead servicing, which keeps print nozzles clear and ink flowing smoothly. In addition, some residual ink is left in the cartridge after it is used. Only use the power cord and power adapter supplied by HP. (Page 1)