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Neem oil is generally quite effective in treating both the aphids and the sooty mold problem. In order to rid the plant of sooty mold, you must first take care of the aphids. Take care to wash off the sticky residue from foliage prior to applying the neem oil, and also coat both sides of the leaves--paying special attention to the backside, as this is most commonly where the aphids congregate. More than one application is often necessary but after some patience and vigilence, this should take care of the problem.

This is sooty mold. It happens when the plant gets a pest infestation. I would recommend using neem oil, as this will get rid of the sooty mold fungus and kill the pests. Here are some articles that will help you: https://www.gardeningknowhow.com/plant-problems/disease/how-to-get-rid-of-sooty-mold.htm, https://www.gardeningknowhow.com/problems/pests/neem-oil-uses.htm

Yellow leaves normally signal that the plant is under some type of stress. In order to remedy the problem, you must first try to pinpoint the issue. This article should help you with that: https://www.gardeningknowhow.com/ornamental/flowers/gardenia/helping-a-gardenia-bush-with-yellow-leaves.htm This article may also help: https://www.gardeningknowhow.com/plant-problems/environmental/plant-leaves-turn-yellow.htm

In order to prune without hurting blooming, you should wait until after the plant's blooms have faded, which should be in the summer. Here is more information: https://www.gardeningknowhow.com/ornamental/flowers/gardenia/when-to-prune-a-gardenia.htm

This article should answer your questions: https://www.gardeningknowhow.com/ornamental/flowers/gardenia/when-to-prune-a-gardenia.htm

Pruning it back will help it. There is not much else you can do to reverse cold damage. These articles will help you as well: https://www.gardeningknowhow.com/plant-problems/environmental/how-to-tell-if-a-plant-is-dead-and-how-to-recover-an-almost-dead-plant.htm, https://www.gardeningknowhow.com/plant-problems/environmental/tips-for-saving-cold-damaged-plants.htm, https://www.gardeningknowhow.com/ornamental/flowers/gardenia/when-to-prune-a-gardenia.htm