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Desert rose prefers growing in warm conditions, so it is only well suited for growing outdoors in warmer tropical and subtropical regions. Otherwise, it is best to grow the plant in containers. Select an area with full sun.

Yes, you can. This article will help:
https://www.gardeningknowhow.com/ornamental/flowers/desert-rose/desert-rose-propagation.htm

If they have developed their true leaves, you can go ahead and separate and transplant them into their own pots. You can save the seeds. Place them in a cool (but not cold) place and they will last for awhile until you are ready to plant more.

Yes, wait for the seed pod to form and then dry out. After that, you can collect the seeds and plant them.

Seed viability is always best the fresher the seeds are, so if you are ready to start growing them and feel you can keep the seedlings happy, you can plant them right away. Otherwise, you can store the seeds until you are ready. They should store well for at least 6 months, and some will even be viable for a year or so if stored well. Here is an article that can help with storing them:
https://www.gardeningknowhow.com/garden-how-to/seeds/storing-seeds.htm

This article will walk you through the steps of growing the seeds:
https://www.gardeningknowhow.com/ornamental/flowers/desert-rose/desert-rose-propagation.htm

I would give them bright, indirect light until they have become well established, at which time you can give them more direct sun.