What are the health hazards associated with the use of separation techniques like paper chromatography or distillation etc?

Depends: These techniques are typically performed in a laboratory, where proper laboratory safety is exercised according to the requirements of the law and the host institution. Speak to your primary investigator, or the lab safety manager to be sure you are taught proper lab safety. The various chemicals you use each have an msds form, that tell you the health hazards of that reagent.