Gas Giant composition

A fellow was telling me that Jupiter and other gas giants are supposed
to be about 99.9% Hydrogen and Helium. I am suspicious of this for
the following reasons:

1. One cannot analize the spectra of the core of a planet, or
anything but the cloud top layer. Do tell me if I am wrong on this,
and how it could be done by us from earth or a human existing
spacecraft.

2. Denser materials will tend to sink to the core of a gas giant.

3. While we can know the mass of a gas giant from the period of
objects in orbit around it, the diameter will be more of a matter of
opinion, as atmopheres do not have very sharp boundaries.

4. We will also not know the temperature gradiant of the planet as a
function of distance from the center. While if we did I could buy
that a computer model could be made that would account for different
densities, not if you are not sure of the temperature gradiant.

5. Nuclear processes at the core (need not be fusion) can mess with
assumptions about temperature gradiants, and said nuclear processes
might involve large masses of Radium, Uranium and Thorium as in the
earth's core, which will all sink to the core of a gas giant as while
some ores of rock with Uranium ect are lighter than the mantle of the
earth, they are all a lot hevier than air or H2 gas.

Comments?