How much shielding is necessary to protect electronics etc. from
permanent damage from the particle flux of solar flares? Or, for that
matter, from cosmic radiation?

I'm assuming that most current satellites do not carry the heavy
shielding required to protect them from strong flares (doesn't look
that way from pictures etc.). What happens to them then during heavy
flare activity? Do they just shut down, roll with the punches, and
then get restarted?

What about all these iron particles travelling at almost relativistic
speeds? Surely that can do a lot of damage to electronics?