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If only the leaves are damaged, but the roots are not damaged, the plant can probably recover. Is the plant in a pot that can be brought inside to protect it from future frosts? If so, trim off the damaged leaves and stems, and also reduce watering since the plant may not be able to use as much water now. Wear gloves while doing this, because this plant's sap is toxic and can irritate skin.

If your plant is outdoors, helping it go dormant by not watering or fertilizing it will help it protect itself from the cold.

https://www.gardeningknowhow.com/plant-problems/environmental/tips-for-saving-cold-damaged-plants.htm
https://wimastergardener.org/article/desert-rose-adenium-obesum/

You are correct! those are seed pods! You should let them go until they, naturally, start to dry. This is a wonderful thing.

Here is a link for propagating those seeds when they are ready: https://www.gardeningknowhow.com/ornamental/flowers/desert-rose/desert-rose-propagation.htm

There are a few things that can cause this. Most commonly, this is due to a lack of light, or Over/under-watering. Unfortunately they can cause the same symptoms.

Here is an article on further care of the plant: https://www.gardeningknowhow.com/ornamental/flowers/desert-rose/caring-for-desert-rose-plants.htm

You will want to put enough soil in the bottom of the new container just enough to bring the plant up to the level it was. Then fill the sides in with soil. It is best to start with moist soil, but will not hurt to water it in after.

This article will give you more information on their care: https://www.gardeningknowhow.com/ornamental/flowers/desert-rose/caring-for-desert-rose-plants.htm

There would be no way for me to tell you what month, exactly, to plant these without knowing your locations. You can plant indoors as long as the growing media remains above 80 F and below 86 F, and outdoors as long as the soil is between that range also. Whichever month in your area stays like this, is when you will be able to plant.

Here is an article that will give you more information: https://www.gardeningknowhow.com/ornamental/flowers/desert-rose/desert-rose-propagation.htm

If you're talking about 'Osiria' Hybrid Tea rose, then you'd following the same rose seed planting guidelines specified here on GardeningKnowHow: https://www.gardeningknowhow.com/ornamental/flowers/roses/growing-roses-from-seed.htm