I think there are three main things to stress at this level about Cherenkov radiation:

1) There must be a transparent medium in order to "see" the radiation.

2) It is produced by particles with electrical charge.

3) The particle must be going faster than the speed of light in the medium.

Cherenkov radiation could be a topic for a student simulation. The game could allow users to select a particle (electron, muon, tau, proton or more exotic not yet seen particles like a magnetic monopole) and produce a light pattern based on some medium properties like its index of refraction, and more ambitious, including absorption and scattering.

There are two answers to what happens to the neutrino when it interacts. The interaction involves an exchange of either a charged boson (a W+ or W-) which changes an up quark to a down quark or vice versa. This W particle has a large mass which means it is not likely to be created if the incident neutrino is lower in energy. Like trying to buy a mansion with a minimum wage job! There might be some unlikely way it occurs but mostly not.

This is called a charged current interaction because the W boson particle is electrically charged. The neutrino is gone, and it corresponding particle is produced (electron neutrino produces an electron, etc.). Since the energies of the neutrinos we are dealing with are so high, there is a cascade of other particles created in the initial interaction in addition to partner particle. But no more neutrinos....except for the case of tau meutrinos which interact, produce a tau which lives a time based on its energy, and then the tau decays producing another tau neutrino. A detail that is important for another reason I won't go into. By the way, we say neutrinos go right through matter but this is only true for low energy neutrinos. Above about 1 PeV, the Earth starts to adsorb neutrinos and we can only look for neutrinos from increasingly smaller part of the sky. Connecting back to Bai's talk, the solid angle seen goes from being 4pi at lower energies to a little over 2pi for the highest energy neutrinos.

It is also possible to create a neutral particle call a Z boson. In this case, the neutrino is not adsorbed in the interaction but changes direction and loses energy. This transfers a lot of momentum and energy to the proton or neutron involved, basically blowing it up producing a lot of very high energy electrically charged particles that produce bursts of cherenkov light before they interact. The net result is a roughly spherical outgoing ball of light. Neutral current interactions become more likely at higher energies (above PeV).