Re: What are the byproducts of Caffeine in urine?

To answer somewhat in reverse order.
Caffeine is a methylxanthine, found in coffee, tea, chocolate and some 
other foods.  These also have the related theobromine and a few have 
theophylline.  The latter, usually as a salt, aminophylline, is used as a 
prescription drug, usually for asthma and sometime other breathing 
difficulties.  Theophylline is the most potent followed by caffeine 
followed by theobromine.  (Potency refers not to how much effect it has but 
to the concentration required to elicit a given effect, thus it takes less 
theophylline than caffeine to relieve breathing difficulties in an 
asthmatic, but caffeine would also do the trick, just take more of it.)

1.  Caffeine can be tested for in the urine, though one would generally 
test for metabolites of it since they would be more common.  The tests 
require instrumentation like gas or liquid chromatographs however.  To my 
knowledge there is no simple colorimetric reaction that would be specific 
for caffeine or its metabolites, or for the related theobromine found in 
chocolate and tea.

2.   Re precipitation tests, if you mean for Ca2+, then there are 
colorimetric tests for Ca2+, but the concentration in urine would generally 
be too small and other, more sophisticated tests would be needed.  If you 
mean precipitation for caffeine, see answer 1.

3.   Caffeine cannot itself directly leach Ca2+ from bone in a chemical 
sense.  As a drug, caffeine has a weak action to release stored 
intracellular Ca2+ into the cytosol of most if not all cells so that some 
(but not all) Ca2+ might (or might not) be released into the general 
circulation and thus eventually find its way to the urine.  The effect on 
bone would be extremely minor and probably not measureable in terms of Ca2+ 
loss.  There are far stronger influences on bone Ca2+ than caffeine.  Put 
another way, I wouldn't worry about whether a couple of cups of coffee will 
give me osteoporosis or brittle bones.

4.   Caffeine is a methylxanthine and is metabolized by the liver by 
demethylation to 1,7-dimethylxanthine (paraxanthine) to 1-methylxanthine 
and by oxidation to 1-methyluric acid.  Acetylation also occurs and it is 
these latter compounds that are found in the urine rather than caffeine 
itself.  Theophylline is metabolized somewhat similarly.