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The cut stem is not likely to root and re-grow. Cut it at the base and carry it out, or remove from the top down in small pieces to make the removal and disposal more manageable. The stump may re-sprout unless you apply herbicide or remove. The stump and underground root system will remain and will be an obstacle for planting in the same spot. Digging out the stump will be a big job. Plant off-center in open spaces to avoid strump removal.

This is, simply, a seal for when the plant was pruned. In a nursery setting, where there are many trees in one spot, it is useful to keep diseases to a minimum.

This treatment isn't, usually, necessary in the home setting.

This will not harm your plant, nor will you need to do anything with it.

Here is an article that will help you to care for them, indoors: https://www.gardeningknowhow.com/ornamental/foliage/yucca/growing-yucca-indoors.htm

Yes

Our experts say to wait until the soil feels completely dry a couple of inches (around 5 cm.) below the surface before each watering. Here's an article to help: https://www.gardeningknowhow.com/ornamental/foliage/yucca/yellow-yucca-leaves.htm

You may want to cut the branch into smaller pieces for rooting. Here's a helpful article;
https://www.gardeningknowhow.com/ornamental/foliage/yucca/propagation-of-yucca-plant.htm

It does appear to be related to overwatering. Make sure that the soil has a chance to dry out thoroughly between waterings. Yucca will tend to prefer dry soils, and this will be especially true indoors.

Here is an article that will help you with their care:

https://www.gardeningknowhow.com/ornamental/foliage/yucca/growing-yucca-indoors.htm