Sounds like the drain in the bottom of the freezer or the tube is clogged. When most self defrosting freezers defrost, the ice melts, runs through a hole or tube in the bottom of the freezer and into a tray under the freezer which is then evaporated from the heat generated by the compressor. if the water cant get to the tray it will eventually run out of the freezer since the defrost timer continues to cycle.
-- If I understand your the problems properly
1) If the water is running down into the refrigerator section, This usually means the drain is blocked. Look in lower section at the top center ( you may have to remove control panel to get access) remove the drain cup gentle with screw driver from each side, clean , from under unit at the back locate the drainage tube, having someone holding paper towel from were you removed the drain cup blow into the tube to clear any blockage that might be in tube, re-install drain cup.
This should clear water leakage problem.
2) Icemaker You may have 1 or a couple problems here. First problem may be the water valve may not be closing fully allowing a small amount of water to continually leak into the icemaker.
Solution Replace water valve
Second; The problem may also be with the freezers defrost thermostat, If this is the problem though it usually means your food is also freezer burnt, Means the unit when in the defrost cycle is staying on to long allowing to much heat to be generated in the freezer compartment.
Solution: Replace the defrost therostat |