Pure water could be separated from inky water in a variety of ways. One option would be to use distillation. Put the inky water in a container and heat the water to boiling. Pass the steam through a cooling coil to convert it back to liquid and collect the purified water.
Another option would be to use a color removing material such as activated charcoal. You could put the charcoal in a tube and pour the water into the top of the tube. As the water filters through the charcoal the inks would adhere to the charcoal and pure water would come out the bottom.
A third method would be to use reverse osmosis. By using high pressure, the water molecules can be force through a membrane but the larger ink molecules would be left behind.
To separate the petrol from the kerosene you would use distillation again. By heating the mixture the petrol would boil at a much lower temperature than the kerosene. As you did with the inky water, pass the petrol vapors through a cooling coil and collect the liquid petrol. You would monitor the temperature of the mixture and once the temperature rose much above 70 deg. C you would know that the petrol had been boiled off. The liquid remaining in the original container would be the now pure kerosene.