How does her power work and what can she do ?
The original Phantom Lady, Sandra Knight of Earth-X, was simply a skilled martial artist with a "black light ray" that blinded her enemies and could turn her invisible when aimed at herself. She also had a gift for... distracting her male enemies. In the Freedom Fighters 15-issue series, crossing over to Earth-1 gave her the ability to turn intangible as well.
Since then, a couple of women have used the name. Dee Tyler (Phantom Lady II) was trained at an actual spy academy, giving her a lot of unusual fighting and infiltration skills. Her black-light ray was an energy blaster and also made hologram copies of her.
The latest, Stormy Knight, is both brilliant and famous. She's still exploring all that her blacklight projector can do, in addition to throwing darkness. It seems to warp dimensional boundaries in some way.