Jupiter is roughly 1/1000 the total mass of the sun. To get some idea of what effect Jupiter's gravity may have on the sun I'd like to know the approximate mass distribution of the sun. (i.e) the approximate mass of the core, the radiative zone, the convective zone and of the photosphere?
All these are answered in the wikipedia article on the sun.
This Nasa link has a recent study of the shape of the sun.
The question in the header:
Has also been answered except it is hard to find links, since googling gets flooded with astrology links and dubious links to barycenter models which are not acceptable. You can find some order of magnitude calculations here. This is an estimate of the combined planetary tidal forces:
Unfortunately they have no scale on fig6 because they are intent in finding correlations with sunspots, but I believe that the scale should be milimeters.
NASA give an empirical formula for the density of the Sun:
$$ \rho(x) = 519x^4 - 1630x^3 + 1844x^2 - 889x + 155 $$
This gives the density in g/cm$^3$, and $x$ is the depth in solar radii i.e. $x = 0$ at the centre and $x = 1$ at the surface.