What happens to the resistance, voltage and current when DC passes through saltwater?

Dissolving salt in the water creates sodium and chloride ions which in the presence of the potential of the battery provide a path for current flow, the movement of charge. Thus resistance is decreased and current is increased.

While an ideal voltage source would see no decrease in the voltage, a real world battery has its own internal resistance, and so you would see a slight decrease in the battery voltage if the battery was fully charged, and more of a drop if not fully charged.

Addition of salt will facilitate the conduction of electricity due to ionization. The extra ${Na^+}$ and ${Cl^-}$ ions will increase the conductivity of the medium.

1)Voltage will be slightly affected if you are considering internal resistance.

2) and 3)Current will increase due to the decrease in resistance in the conduction medium.