Thank you all for your suggestions.
I have also thought of installing the XP tank but I did not fully understand their funciton. I also thought of installing the check valve but wasn't for sure if it would cause excess pressure on the tank. The tank does have the pressure valve on top for safety.
As for the cold water drip tube, I have removed and inspected it. I found no cracks or holes that should not have been there.
A cousin suggested to make a loop in the cold water line right before it goes into the take. He called to a dog loop. He said sometimes the hot water will not get past the loop but it doesn't explain the problem I am haveing.