with regards the repeated stating that zombies, being dead, will rot and decompose quickly. This is something that was addressed from day 1, why do zombies eat living flesh, and not each other? because it provides them with the living matter that they need in order to not decompose. Deprive a zombie of living flesh for a while and yes, they will start to decompose and "die", but otherwise, their status as undead does not diminish them in that capacity.
As to zombie strength, well, with the impaired nervous system, it is not so much strength that you would fight against, it is as has been previously mentioned, the lack of pain sensation and instinct for self preservation. With many zombies utilising their limbs in a club-like manner. A number of effective counters to zombies, can be employed by overcoming the human instinct to not cause lasting injuries, and to aim squarely for the joints, a sharp stamp to the kneecap, will cripple most zombies quite effectively.
Again, as mentioned previously, zombies cannot swim, although they can walk along the river/seabed with relative ease, albeit rather restricted by currents, and some particular types of fish. That being said, zombies are instinctual hunters, and are unlikely to follow for very long before losing interest.
And finally to senses, while zombies retain all of their core senses, they are reduced to the level of an instinctual hunter, they can see their prey to hunt it, they can smell and even hear them, but do they know to associate lights on in a window with the presence of their quarry? Its hard to say, possible, but unlikely. What is more likely is that they follow the scent trail and that leads them to the same place.