At what total rate is water used in metabolic processes over the entire biosphere?
The lifetime of a water molecule is less than 1 millisecond, in the sense that two particular protons will not remain bonded to same oxygen ion for longer than that order of time.  Also, the protons of water are constantly exchanging with protons of other molecules and ions, such as alcohols, amines, carboxylic acids, bicarbonate, and countless acids.   So it would only make sense to discuss the rate at which the oxygen atoms of water become atoms of another substance (beyond just hydroxide or hydronium) such as dioxygen or sugar.  

For photosynthesis, one molecule of water is consumed for each molecule of carbon dioxide.  The link says that about 110 billion tons of carbon undergoes photosynthesis per year and since a water molecule is 1.5 times the mass of a carbon atom, this means 160 billion tons of water consumed in photosynthesis.  

So at a minimum, biological processes destroy and create 160 billion tons of water per year (on the basis of whether an oxygen atom is or isn't part of a water molecule).