It runs fully sequentially, but there is good potential to parallelize parts of it. This is something I'm working on actually.
Yes, I think so. Sadly, I personally don't know enough about it to implement it myself, but I know that there have been experiments/attempts by others in the past.
Depends on what. Rendering and simulation are on the same thread, pathfinding runs in multiple threads. Sound is in its own thread. The OS decide which threads goes onto which core. @vladislavbelov is working on a way to run the rendering on parallel to the next simulation turn. That will help although on higher end machines, rendering isn't so hard on the GPU.
When you mention render submission being the main bottleneck, is the core issue that Pyrogenesis's rendering pipeline runs sequentially on a single CPU thread, or is it already multithreaded and just struggling with massive draw call volume late-game? Furthermore, is there any prospect for optimization through GPU instancing to batch identical units and cut down those draw calls?