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Plumerias do not like temps below 40 F., so just to be on the safe side, I would at least wait until the temperatures outside rise a bit more, say 50 F. or more, and remain consistent.

Yes, a change in temperatures would bring about stress such as this. It should right itself, however.

I would check the moisture of your container soil, which should be moist not wet. Also, big drops in temps, especially at night, can trigger bud drop. I would check for insect pests as well.

If the plant is in very bright sun, it is possible that the oil worked with the sun to burn the leaves. Make sure you are diluting the neem oil to the right mixture and then try applying in the evening, so the mixture has time to be absorbed before the sun comes up. You may also have another issue with the plant, perhaps a pest or a different disease. I would examine the leaves closely for signs of pests. It would be difficult to diagnose from here what is exactly wrong with the plant, as there are many, many things that could be causing yellow leaves.

Pruning for these plants is normally achieved prior to new growth (late winter/early spring for us in the US, so likely opposite season in your growing region). They can be pruned as needed to 12 inches from the ground (or soil in pot). This will help balance out the new growth the following growing season. For more information on growing frangipani (Plumeria) plants, this article will help: https://www.gardeningknowhow.com/ornamental/flowers/plumeria/growing-plumeria.htm

Yes, you can take cuttings, but I would do so now. These articles will help: https://www.gardeningknowhow.com/ornamental/flowers/plumeria/growing-plumeria.htm,