1. Pretty close
2. Also, pretty close
3. Close in the lower ISOs, then the 1Dx separates itself
4. IMO, not even close. While the 5D3 is pretty snappy, I don't find it to be anywhere near as fast in speed or accuracy. The 1Dx drives lenses, while the 5D3 negotiates and gets where it gets. I also believe the 1Dx is slightly better in lower light. Yes, they use the same system, but it is not the same system.
So, depends on what you shoot. Wildlife, sports - 1Dx. Portraits - 5D3.
This is MY OPINION having used both cameras in a multitude of scenarios. Both excel, just in different areas. I've considered selling my 1Dx and moving to the 5D3 for a lighter weight body paired with my 1D4, but just can't do it. For what I shoot, I'd lose too many features that I like having.