Answer 1:
In principle, this technique might work.
However, you would need to consider several
factors:
Does the density of new ostrich eggs vary
significantly from 38 g/cm^{3}? Does the
rate at
which ostrich egg density declines depend on how
the egg was stored? Does this rate depends nn
variability in the egg itself?
Essentially, you would need to find the error
associated with eggdensity dating, likely by
constructing a calibration curve (year vs.
density) of eggs stored in a similar manner with
known density and dates. The 'width' of this
plot would tell you whether or not your method
is accurate, and you could find a standard
deviation to give you an expected error
(and "proof"  actually a confidence interval 
that your egg is a certain age).
I would guess that natural variations in eggs
and the storage method would render your
technique less accurate than other methods for
dating organic samples: see "amino acid dating"
or "radiocarbon dating".
Best,
