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Each of the seedlings should have 6 true leaves before transplanting to new pots.
Desert Rose do better when they are more root bound so do not choose to large of a pot. A pot size that is 6 to 8" in diameter.
Choose an unglazed pottery or clay pot as this will help the soil dry out between waterings.
Fill the pot with a good quality potting mix--you can mix a potting soil with equal parts of cactus potting mix.
Gently remove the seedling and place the seedling into the new pot.
Firmly press the seedling into it's new soil mix.
Water lightly but make sure the soil is moist and not soggy. Root rot will take over quickly, so do not over water.
Keep the pots in a warm location- 75 to 80 degrees F, do not allow the plants to be exposed to temps below 40 degrees F.
Full sun location with at least 8 hours of sunlight.
After you began to see new growth you can a balanced fertilizer application ever couple of weeks until it flowers.
Here is a link with care information.

https://www.gardeningknowhow.com/ornamental/flowers/desert-rose/desert-rose-propagation.htm

Unfortunately some supposed rose seeds simply are not, they may be other seeds or in many cases just clumps of dirt and organic matter. There would be no real good reason to do such a soaking with rose seeds that I can think of. See this link for an article I wrote on rose seeds: https://www.gardeningknowhow.com/ornamental/flowers/roses/growing-roses-from-seed.htm The seeds need that cold period to perform as desired.

Many roses have reddish new growth which makes identifying rose rosette virus difficult. Judge yours in relation to other canes. One hallmark I kept reading about was the superabundance of thorns on infected canes which isn't apparent on your pictures. But is this very early infection? I found this website had good information and pictures as well as detailed description of signs of infection.
http://www.clemson.edu/extension/hgic/pests/plant_pests/flowers/hgic2109.html

The color of the growth is fine but may need a bit more water if that wilted on the bush in the ground. No cause for concern that I see at this time. No distortions of the foliage that would indicate rose rosette disease that I see. Give the rose bushes a boost by watering them with some water that has both a product called super thrive and a root stimulator mixed in the same water. Give them a fresh batch of this mix the next 4 to 5 times they need watering for a nice boost and good bloom production.

Yes, I do trim off any growth by the potato itself as it can just interfere with the rose getting going well.

Sounds like Blackspot.you can prune away spotty leaves and use certain sprays. Lime sulfur and copper are a more organic option than chemicals. Keep your garden clean and water in the morning. Inspect your rose daily.