Can two singularities combine into one? We know that black holes can collide and merge, but if they each have a singularity at the core, how can the two singularities merge and become one? Wouldn't the mere fact of a second singularity in range of another make it not a singularity?
Hypothetically, Yes. Realistically, No. As James mentioned a singularity isn't a physical object but rather a point in space time. In theory a wormhole is just two singularities which combined.