Are there mood disorders only women get?

Not Really. While depression is more common in women both genders can certainly get it. In the past they used to speak about women being more likely to show their depression through sadness & men through anger. The incidence of bipolar disorder is equal for both genders.
Sort of. All major mood disorders occur in both sexes with a slightly higher percentage in women. A form of depressed mood that only occurrs in women would be pre-menstrual dysphoric disorder which occurs starting a week before menses. This is classified as being different from being "pre-menstrual" the other disorder would be depressed mood related to menopause.
There are . Probably the most common one that comes to mind is premenstrual dysphoric disorder which is like severe PMS. Since only women have a period only woman can suffer from this.
Estrogen progestero. Both sexes get depression and both kind unipolar and bipolar kind the expressions are different due to hormones .Also the sex ss also sit on serotonin receptors which are happy juices so as we age the sex juice goes down so does the happy juice . Pregancy mentrual cycle and menopause have the same impact , boys have same cycles , but no physical signs to go with it but they have menopause too.