If a satellite covered with a thick layer of copper, were to go straight through a solar storm in the opposing direction, would the satellite produce electricity, provided the copper(or other suitable material) doesn't melt? Could the satellite harvest this energy? Can this be used to study solar storms further?
in my opinion it should, by laws of electromagnetic induction, but I am asking this to know whether it would be practically possible?
You need both a source and a sink to produce electric current by electromagnetic induction, otherwise you're really just a target at the mercy of the incoming energy discharge. So if you're going to have large static collectors in the way of high-energy electron flux of solar storms (pretty broad definition), you better have ways to use, store or convert all of that energy to some useful purpose, otherwise it's going to build-up on static charge and can damage your equipment by destructive electrostatic discharge.
But yes, the energy in solar storms, as you put it, could be converted into something useful, like electricity. Problem is, they're rather unpredictable in both time and intensity, and we can already convert solar radiation energy into useful forms with simpler, proven technology (e.g. photovoltaics), measure proton flux with various particle detectors, magnetic fields with magnetometers, heat with thermocouples, infrared sensors, ad infinitum. And then there's the use of solar radiation pressure for propulsion with solar sails, attitude control by magnetic fields with magnetorquers, even electrodynamic tether propulsion (PDF).
But all these systems have one critical thing in common: They can either be deactivated, protected, or the whole energy they collect is used, converted, stored or dumped so the electric fields don't build-up as static charge. The latter is a bit of a problem in the vacuum of space, and that's why such charged particle flux is really more of a hindrance to space exploration missions with precious and sensitive equipment onboard, so they rather try minimizing their potentially mission-ending effects, than consider them something worth waiting for. Unless you're actually measuring it, usually from a relatively safe distance and well protected, like SDO and the two STEREO spacecraft do while performing their heliophysics observations of our Sun.
