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It sounds like it might be mealybug. This article will help with that:
https://www.gardeningknowhow.com/plant-problems/pests/mealybugs-white-residue-on-plants-leaves.htm

If it's powdery in nature, however, then it could be powdery mildew. Here is more information: https://www.gardeningknowhow.com/plant-problems/disease/powdery-mildew-homemade-and-organic-remedies.htm

The wet soil is likely the problem. Wet soil that freezes in the winter is very hard on the roots of plants and it actually what kills more plants in winter than the actual cold. They are suppose to stay green, but if the stems are alive still, it may regrow it leaves. This article will help you determine if the plant is still alive: https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm Beyond that, I would either try to improve the drainage in the area before planting the other one or choose a new, better draining location.

I would suspect possibly chlorosis. This article will help: https://www.gardeningknowhow.com/ornamental/shrubs/holly/holly-yellow-leaves.htm Regardless, I would fertilize and also treat the plant with a fungicide, as these two things will help fix many of the other possible causes for the unhealthy plants.

This article should help: https://www.gardeningknowhow.com/ornamental/shrubs/holly/holly-yellow-leaves.htm

From my research the Princess Blue Holly berries generally start a bright red but will turn brown to almost black...but generally this will happen during the winter.
If the Holly appears healthy I would not be concerned over the color of the berries.
Holly berries can be reds, burgundy's, browns, blacks and rarely yellow and green.

https://www.gardeningknowhow.com/ornamental/shrubs/holly/how-to-tell-the-difference-between-a-male-and-female-holly-bush.htm

Yes, you do have to have both male and female plants to produce berries on the female. The female will produce flowers without a male nearby, though. This is true of Princess varieties as well as most holly varieties. There are also a few parthenocarpic varieties, meaning the female can produce berries without being pollinated by a male.

https://www.gardeningknowhow.com/ornamental/shrubs/holly/how-to-tell-the-difference-between-a-male-and-female-holly-bush.htm