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I am not certain which caterpillar it is. This site can help you identify it:
http://www.whatsthatbug.com/

But all caterpillars can be controlled with Bt. This article explains more:
https://www.gardeningknowhow.com/plant-problems/pests/insects/prevent-caterpillars.htm

There are 2 plants that are referred to as Angel Trumpets, datura (flower points up) and brugmansia (flower hangs down).

Both cannot be divided in the traditional sense of the word, but daturas often reseed themselves in clumps, so there will be several plants growing in one location. These plants can be separated. Just check for multiple stems coming from the ground and each stem is a different plant.

Brugmansias are most often propagated by cuttings. They are SUPER easy to root. Here is an article on that:
https://www.gardeningknowhow.com/ornamental/trees/brugmansia/tips-for-propagating-brugmansia.htm

This article may help: https://www.gardeningknowhow.com/ornamental/trees/brugmansia/growing-brugmansias-in-containers.htm

Assuming that the plant is well-watered, this may answer your question:
https://www.gardeningknowhow.com/plant-problems/environmental/plant-leaves-turn-yellow.htm
And more here about angel's trumpets:
https://www.gardeningknowhow.com/ornamental/trees/brugmansia/growing-brugmansias-in-containers.htm

You have a brugmansia. This article will help:
https://www.gardeningknowhow.com/ornamental/trees/brugmansia/growing-brugmansias-in-containers.htm

It is most likely a lack of water causing the flowers to fall off. They are water hogs and need lots of water to stay healthy.