the cathode should produce hydrogen gas, leaving hydroxide ions, and sodium, which reacts with the hydroxide ions to give sodium hyrdoxide solution, this then reacts with the chlorine to give sodium hypochlorite. if you want to get chlorine and sodium hydroxide you need to keep them separate by using permeable diaphragm (unglazed pottery would do like a plant pot) so they do not react. you could then use the hydrogen and the chlorine given off to produce hydrogen chloride, perhaps using a tubes with a flashback arrestor installed for safety (a cigarette filter would do) and bringing them together and lighting them, they would burn together and you could collect the hydrogen chloride produced (i don't know how affective this would be i've never tried it)
To get sodium you have to do electrolysis of molten sodium chloride (which melts at about 800 degrees celcius) or molten sodium hydroxide (which melts at a lower temperature but its a dangerous chemical itself) and then you have to make sure the sodium doesn't come into contact with air or water because it is so reactive, so you'd be better off not attempting this.
Merged post follows:
Consecutive posts mergedthe colouration could be the chemicals reacting with the cathode, what material did you use?