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It is soil where the water will run mostly out. This is normally done with a 2:1 mix of potting soil and either sand or vermiculite.

sounds like it is dead to me but what zone do you live in? Mine lives for several years then a heavy snow year seems to kill it/break it but I live in a moderate but wet climate on the west coast zones 5/6 & my rosemary usually grows year round. Cut it way back & see if new growth appears & if not time to get a new one.

This is powdery mildew. This article will help:
https://www.gardeningknowhow.com/edible/herbs/rosemary/white-powder-on-rosemary.htm
https://www.gardeningknowhow.com/plant-problems/disease/powdery-mildew-homemade-and-organic-remedies.htm

You won't have much luck by simply sticking rosemary in water. However, the following article should be of some help to you:
https://www.gardeningknowhow.com/edible/herbs/rosemary/how-to-propagate-a-rosemary-plant.htm

It could be powdery mildew or a pest. This article will help you with powdery mildew: https://www.gardeningknowhow.com/edible/herbs/rosemary/white-powder-on-rosemary.htm

It may also be pests, possibly mealybugs. This article will help with them:
https://www.gardeningknowhow.com/plant-problems/pests/mealybugs-white-residue-on-plants-leaves.htm

Hum well there is one that grows straight up, I just got my hand on the one that
has a weeping growth. But rosemary is rosemary, you can use it in your hot bath, fill you tub and put a bunch of fresh cut rosemary.
it will ease your fatigue and pains.
Sniff I dont have a tub!! lol I tried this when I lived in an apart. and it was great
it was a bath foam with rosemary.