If you want to research you should start reading the specific literature.
Hope you don't mean me. I know the theory but have no direct experience with breeders. And from my understanding the ones that have been built have not been all that successful. There do seem to be a lot of resources online so start there.
If so, here.
Unlike me many people here can answer on your questions regarding fission reactors.
I think that some of them are experts in this field.
I would recommend you study nuclear engineering.
Most nuclear physicists study the nucleus and other subatomic particles like quarks Some nuclear physicists are more applied science and work on nuclear reactors, but you won't find many.
There has been a lot of experience with breeder reactors. I am sure there are several things that need more understanding. Yet, they are a lot of engineering problems to increase the performance of breeders.
The nuclear physics of breeder reactors is well understood.
The engineering aspects are more challenging. Study nuclear engineering if one wishes to do research concerning breeder reactors. Look at courses in reactor physics (neutron transport theory), materials science, mechanics of materials, fluid mechanics/dynamics, corrosion, . . .
Separate names with a comma.