Oh my, the hughester is in for it....
OK the plant thing: not capillary action so much as evaporative pumping. Transpiration powers it.
The menstrual thing: the moons gravity is used by the female body to provide a timing effect, but women do get by without it, though with more irregular periods. Also great numbers of chicks in the west regulate their menses by the pill, not the moon. Frostbitten: without ocean currents no life at all. Circulation of nutrients essential. Many would run though, due to thermal effects. The biggest change would be atmospheric. The moons gravity effectively thins out the atmosphere of the earth. Without it we would probably be much more like venus (boiling sulphuric acid rain, anyone?). Consequently our kind of life would not be here. If it suddenly left: huge seasonal variations and massive climate damage. Probable thinning out of or extinction of humanity as a result. Many insect species unable to breed, many flowers and trees die off. unpleasant.