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I am seeing a lot of this at this time of year. This is a fungal infection, and since it is in container, you can control this fairly easily. Just use peroxide at 3 parts water to 1 part peroxide when watering the next time. Make sure that you let this dry pretty well between watering, as too much water is usually the cause of this.

As for the thing falling over... You can control its growth by keeping it confined in smaller containers. They will explode with growth if you give it room. They like to get rootbound, so you will be able to keep it in the same container for a few years before doing any work to it.

For now, you can cut the tops off of the leaders that are too tall. This will not hurt the plant at all. You can take these, and root them in soil. They root very easily. This will give you copies of the plant.

This collection of articles will help: https://www.gardeningknowhow.com/houseplants/rubber-tree

This article will help you.

https://www.gardeningknowhow.com/houseplants/rubber-tree/repotting-a-rubber-tree-plant.htm

No, you can't make the plant grow leaves onto the lower stalk or branches.
You can prune the plant to create a fuller plant.

https://www.gardeningknowhow.com/houseplants/rubber-tree/prune-rubber-tree.htm

Artificial light may help, but if you can get it outside to some real sunshine that would be best.

Rubber trees need repotting when the roots become visible on the soil surface or if the plant begins lifting itself out of the pot. Repot the plants in late winter or early spring when the rubber tree is semi-dormant and less prone to transplant shock.
If you don't re-pot your plants, they will not grow. However, don't put rubber plants in pots that are too big. Transplanting to pots that are about an inch bigger in diameter than the previous pot is a good rule of thumb.

It appears to be a variety of rubber plant, which is a type of ficus. There are many kinds, and you happen to have one of the more interesting colored of the tropical looking trees.

This article will give you an idea on how to care for rubber trees: https://www.gardeningknowhow.com/houseplants/rubber-tree/how-to-care-for-a-rubber-tree-plant.htm