Does the Extraterrestrial Alliance make use of spells and curses?

This they do not do in the way of human practitioners of the dark arts. They do not engage in superstition, as they are entirely a logic-based group of beings who make all choices and decisions based on what will happen in the moment that is of advantage to them, and do not seek any ulterior sources of outside energy to work in tandem, other than the dark spirits which to them is simply using a kind of technological and energetic tool. They are conversant with many quantum forces and electromagnetic energies of all kinds, so they can do many things with their thoughts, but these are more akin to a direct assault rather than a curse or spell per se.