After childbirth, it takes few months before resuming menstrual cycles, especially in lactating (breast feeding) mothers. Therefore, don’t worry if your wife did not get her periods within 2 months of her caesarean section. Her periods will return.
She cannot be going through menopause if only one of her ovaries was removed. The other (remaining) ovary will produce enough hormones for her. Essentially, losing one ovary does not cause any hormonal imbalance or symptoms so long as the other ovary is normal. Please chase up the result of the ovarian cyst, which was removed to see if any further treatment is needed.
All (physiological) changes, which take place during pregnancy return to normal, non-pregnant levels in six weeks following the childbirth. Therefore the other symptoms, which your wife is suffering from could be because of some medical condition unrelated to her pregnancy or childbirth. These symptoms could indicate premenstrual tension (syndrome) and she may possibly get her periods soon or could be because of common medical conditions such as anaemia. I would advise you to see your general practitioner and get some basic tests done to find out any co-existing medical condition.