HC and soot emissions are not proportional if that is what you mean. For example, HC emissions can be quite high while soot emissions are close to zero in spark ignited engines while the opposite can be true in compression ignited engines. If you want an accurate and comprehensive measurement of engine performance with respect to emissions, you must measure both.
Probably not. However, if you are analyzing well designed engines running as they are intended to run, the HC emissions from CI and the soot emissions from SI engines should both be near zero. In off design running modes or if the engines are poorly designed or built or have been damaged, these statements are both incorrect.
You need to measure both as their genesis are different. You can check the book Heywood for details but soot mostly forms due to 1) lack of oxygen 2) longer breakup-length of the spray 3) wall wetting- spray hitting the piston walls and etc. HC mostly forms in low temperature, over-lean regions and fuel trapped in the crevices
So in case of diesel engine, mostly you need to concentrate on the HC emissions in loads which are ~30-40% of full load. As the temperature and peak pressures increase the HC emissions in diesel engine are minimal.
Feel free to ask your questions, I will be eager to help
You can read my paper for your reference.
Behaviour Study of Particulate Matter and Chemical Composition with Different Combustion Strategies
Sometimes there is no harm in assuming soot and HC emissions are proportional to each other in CI engines where optimization of design/ operating parameters is being done. But once we get the desired emission characteristics (NOx and soot) we should also need to check for the HC and CO in order to ensure that they also are in the prescribed limits.