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Many volumes have been written and countless have been spent in honing the process of rooting woody ornamentals. There are as many theories and opinions of the process as there are people doing it. A lot of times, it's pure luck, sometimes, it is trial and error, but always success is a "good thing". I don't think an insecticide would have a great deal to do with root development.
Plant material, media, humidity, hormone and temperature are the 5 most important variables in woody propagation. This link might help: https://www.gardeningknowhow.com/garden-how-to/projects/rooting-plant-cuttings.htm

If it's white and powdery, the plant likely has powdery mildew. This article can help with that: https://www.gardeningknowhow.com/plant-problems/disease/get-the-cure-for-powdery-mildew.htm

Without a picture, it is hard to say what it is. I would guess it is either leaf galls, which can be caused by fungus, bacteria or very small pests. If it is leaf galls, they are unsightly, but harmless. More info:
https://www.gardeningknowhow.com/plant-problems/environmental/treating-leaf-gall-on-plants.htm

It may also be a condition called witches' broom. This is typically caused by a disease. This article has more information:
https://www.gardeningknowhow.com/ornamental/trees/tgen/witches-broom-disease.htm

Sounds like it may be a thrip problem. They often attack the base of flowers, causing them to fall when in bud or right after bloom. This article may help:
https://www.gardeningknowhow.com/plant-problems/pests/insects/controlling-thrips.htm

It may also be an environmental issue, like too little water or too much water. Check the soil and make sure that it is not too wet or dry.

This is sooty mold. It is a byproduct of a pest infestation, likely aphids or scale. This article will help you with getting rid of it: This is sooty mold. It is a byproduct of a pest infestation, likely aphids or scale. This article will help you with getting rid of it: https://www.gardeningknowhow.com/plant-problems/disease/how-to-get-rid-of-sooty-mold.htm Neem oil can help as well. In addition to treating whatever pests may be affecting the plant, it is also a good fungicide. Here is more information: https://www.gardeningknowhow.com/problems/pests/neem-oil-uses.htm

As long as the branches are still living (bend easily rather than breaking off), the plant should bounce back once it warms back up again in spring. Here is an article that you may find helpful: https://www.gardeningknowhow.com/plant-problems/environmental/tips-for-saving-cold-damaged-plants.htm