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I recommend that you don't cauterize the plant wound.The heat will cause damage to the surrounding tissue where the callus formation originates and with the heat treatment you will cause a setback not an expediting of the wound closure.

Yes, your jade cuttings could be smaller.

https://www.gardeningknowhow.com/houseplants/jade-plant/propagating-jade-plants.htm

https://www.gardeningknowhow.com/ornamental/trees/tgen/wound-dressing-on-trees.htm

If only one leaf is affected this way, and if its a lower leaf, then it may just be senescence, natural loss of an older leaf. The leaf discoloration and distortion is not characteristic of common pest or disease issues of plumeria that I know of, so it is more likely an environmental issue like watering too much or too little.
What kind of container is it in? Does it have good drainage and being watered appropriately? Even being too close to a window or door could give it an exposure to cold air that could cause this.

https://www.gardeningknowhow.com/ornamental/flowers/plumeria/growing-plumeria.htm

They all look to be suffering from a fungal/bacterial infection.

It is best to make sure that all containers have drainage holes to let all extra water out. If the containers do not have drainage, then this will be to blame. Sitting in water for extended periods will cause root rot, almost always, unless the water is aerated.

I would recommend treating with a fungicide. This article will help: https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm

If any of the containers lack a drain or the ability to rid itself of extra water, then I would switch containers to one that does. You could also just keep those containers from getting any water until they are dry almost all of the way down. This would be an alternative to switching pots.

No leaves, no need for grow light. The light is to facilitate photosynthesis which only happens in the green leaves. But keep an eye on it in early spring when it may start to leaf out.

You can remove the infected leaves and the plant is not likely to die. It will re-foliate. But the new leaves will become infected if you don't initiate a preventive program. Sanitation is important, picking up and disposing of infected leaves that have dropped, as well as picking of infected leaves from the plant.
Preventive treatment includes good soil and water management, including fertilization to build plant nutrition and resistance to pests and disease.

https://www.gardeningknowhow.com/ornamental/flowers/plumeria/plumeria-plants-with-rust-fungus.htm

Often, this has something to do with the amount of light the new plant receives compared to the original. If the cutting is in a place with even slightly less light, this can happen. It is not detrimental.

There are a few other factors but this is the most likely.

https://www.gardeningknowhow.com/ornamental/flowers/plumeria/growing-plumeria.htm