Does all female animals have menstrual cycles?

No. Only humans and closely related species such as chimpanzees have a period or menstrual cycle. Other mammals that have a placenta have a similar oestrous cycle, where the lining of the uterus is built up in case of pregnancy over a specific time cycle, but they don't shed the lining of the uterus as blood in the way humans do, they simply reabsorb the unused uterus.