CAN I DEDUCT THE EXTRA AMOUNT ON MY WATER BILLS FROM MY RENT, DUE TO MY LANDLORDS NEGLIGENCE/NONCOMPLIANCE AND IF SO WHAT IS THE PROPER WAY TO GO ABOUT IT?
Generally, deducting anything from rent just gets you evicted for non-payment of rent.
If there is any procedure for that it would be in the GA landlord tenant statutes:
Unfortunately, I'm not sure I see you winning on this issue because there were some things you could have done (and should have done) to reduce your water costs once you realized the toilet was still running.
1 - There's a shut off valve under the tank. You should have used that.
2 - You should have called a plumber as soon as the landlord became a problem. Those toilet valves cost about $12 and take about a half hour to install. Sure, you might have paid $50 to $100 but that would have been an improvement over 4 months of high water bills.
3 - There is likely something in the statutes that give you the option of giving the landlord written notice that you would do the repairs if he didn't and then deduct from the rent. That would put you in a strong position for the plumbing bill, but not the water cost.
But since you didn't take any measures at all I'm not sure that you are on firm ground for the difference in the water bills now, since that could have been avoided.