Do women have a Yeitzer Hara? Does Shmiras Einayim also apply to girls and women? Or, is it only a male problem?

Are the Halachos of Shmiras Einayim more lenient for women than for men, and if so, why?
What’s the big deal about having thoughts, if they are only thoughts?
Is it permitted for a woman to gaze at men?
How – and from what age – should we educate our girls to stay away from inappropriate materials?
Practically speaking, are the schools seeing this Shmiras Einayim problems in the girls?