Does shmiras einayim apply to women? If yes why?
There is no formal prohibition of hirhurim — improper thoughts — for women. However, it remains forbidden for them to think of zenus, forbidden relationships (based on Iggros Moshe, Even Ha-ezer 1:69), and some write that all lustful thoughts of men are prohibitied (see also Chut Shani, Tzenius p. 48).
Therefore, the basic principle of shemiras einayim, which obligates a person to avoid seeing immodest figures, does not apply to women. However, women should not intentionally gaze at men (or women) in order to reach arousal. Even if this does not cause them actual lustful thoughts for men, it would certainly be improper to awaken desires in this manner.