Could a comet be composed in such a way that its core would be significantly protected from cosmic radiation?

Question

1. could it have a lead bearing rock at its core?

2. how massive would it have to be for the ice itself to protect the core?

3. has a comet ever exhibited a magnetic field?

4. could the "dirt" in the ice ball be infused with enough granular lead, etc. to protect the center?

Answer 1

1) It's unlikely that a comet would have lead in its core.  Comets are bright with big tails when they come near the sun because they are made mostly of ices and lighter elements.  They are not big enough to have differentiated cores, that is, metal cores with rocky or icy mantles.  Even metallic asteroids will generally be made of nickel and iron, which are very common.  Lead is quite rare compared to those elements.  So it's very unlikely that a comet would have any lead.

2) Comets can be many kilometers across, and that should be enough to stop most of the radiation, I would guess.  Neutrino detectors on Earth are about 1km underground for exactly this reason, and get essentially no radiation.  

Most radiation is stopped by a very small amount of material, and so the normal comet material would be enough.  

3)  Probably not.  Magnetic fields require some sort of dynamo action, and comets are much too small.  It's possible that they have a small effect on the Solar magnetic field near them, though.

4)  It's very unlikely.  See point 1.  Also, keep in mind that cosmic radiation can be very high energy, so your intuition about lead being the best way to stop it could be wrong.  Sometimes, metals make the radiation more damaging by turning small, energetic particles into a shower of secondary particles.