I believe you may have come to the correct conclusion as it does sound like the difference in varieties is the likely explanation as to why some of your daffodils bloom and others do not. Some varieties require a longer cold treatment than others (or lower temperatures). For example I have read that Mount Hood performs better in colder climates, and have noted that after particularly mild winters I sometimes see fewer blooms.
As to how long to leave the bulbs undisturbed, that also depends on the cultivar. Some increase much faster than others and need dividing more frequently- perhaps every 3 to 5 years, while others are much slower. Some varieties tolerate being crowded better than others, which allows them to continue blooming profusely when they are crowded. These varieties can be left undisturbed indefinitely or until you note decreased bloom (unless you would simply like to spread the bulbs to other locations or share them with others). Planting the bulbs deeper keeps them from increasing as quickly.
If your soil is fairly fertile, daffodils don't need much fertilizer. Vigorous varieties that naturalize easily may never need feeding, but others benefit from light feeding. I only fertilize mine lightly every 3 or 4 years, and prefer to do so in fall when they are breaking dormancy and root growth has begun. I use bone meal, and often feed other perennials near the bulbs in spring too, so they sometimes get a light feeding in spring just as the foliage begins to emerge. I think 15-15-15 may be a bit heavy on the nitrogen for most flowering bulbs. The bone meal I use is 6-9-7, but any bulb food or flowering plant food with more phosphorus (higher middle number) is good for daffodils. I agree that feeding when the foliage is yellowing seems inadvisable as this is when they are going dormant and essentially going to sleep for a few months. This is the time when cultivated bulbs are being harvested and dried to be stored in temperature and humidity controlled environments until fall planting time.
