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Yes, most varieties can be grown indoors or outdoors, so it is perfectly safe to leave this plant outdoors, even planting it in the ground if desired. You may want to insulate the container with a blanket or other wrap in winter for addition cold protection, as potted plants are more prone to cold damage than those planted in the ground. Pruning your yucca may also be in order. Here is an article that you may find helpful: https://www.gardeningknowhow.com/ornamental/foliage/yucca/yucca-plants-care-and-pruning-tips-for-pruning-a-yucca.htm

As long as there are still some remaining roots left intact, I believe it will recover. However, just in case, you may want to take some cuttings of the plant. This article will help with that: https://www.gardeningknowhow.com/ornamental/foliage/yucca/propagation-of-yucca-plant.htm

Yes, you can move the plant indoors for overwintering. Rather than watering on a schedule, check the top of the soil instead (poke finger into top inch of soil). If the top of the soil feels dry, your yucca needs to be watered. If the soil feels wet, it does not need to be watered. In winter, the plant will need less water, as indoor plants go dormant when the weather cools and only need monthly watering.

Water indoor yucca plants only when the top inch of soil is completely dry. Also, do not allow it to stand in water, as this will lead to root rot.

There are several things that can cause this. When you describe your watering habits, I am leaning towards root rot. Yuccas like their soil a a little dry, so if you have been watering without checking the soil, it is possible it got too much water and has root rot. This article will describe more about root rot and how to correct it:
https://www.gardeningknowhow.com/plant-problems/disease/treating-root-rot-gardening-tips-for-housplants.htm