I don't work in this space anymore. Some I can't talk about but part of what I can talk about is still a pretty big problem, which is finding layer ordering, materials, thicknesses, etc of the shielding. You have problems like that neutrons are absorbed differently than protons, alpha particles, and beta particles (all those are charged). So you want to use thing like hydrocarbons for neutrons (read plastic) and you probably want to dope it. BUT there's a big problem that the energy level matters a lot. Gadolinium is known as having a good neutron cross section, but that is only for thermal neutrons and hot neutrons (as you'd find in space) don't see gadolinium differently from dense materials like titanium and aluminum (good for charged particles). So the problem is to layer, dope, etc. And to do that while accounting for secondary factors like that you can have materials become hot as exposed to radiation and then you also have to consider physical shielding. The solution space is extremely large and you search it by simulation.
As for getting electricity you can probably imagine that if you have two conductive plates that they will get charge levels across them and that's a capacitor. There are other ways to extract energy though and finding ways to do this is very helpful. But there is a theoretical limit to the energy and don't expect to replace solar panels unless you can capture those particles and use a nuclear process instead of an electromagnetic one.
If you're interested in this start searching for betavoltaics[0]. That uses the E&M process whereas an RTG uses a thermal process. There's nothing stopping you from using both though.
