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Plants that have been frozen often lose all or most of their leaves, but they still have a good chance to recover. The best option is to leave the plant alone and see if it perks up over the next few weeks or even months. Don't give it any more water or fertilizer until it shows signs of recovery or until the soil feels very dry to the touch. Damaged plants will often slow down their water and nutrient usage to almost nothing.

If the leaves turn completely brown or dry, you can cut them off. Eventually, the plant should produce new leaves if it's alive. If it doesn't, try cutting back the trunk to a part that is visibly living and let it regrow from there.

https://www.gardeningknowhow.com/ornamental/foliage/yucca/yucca-cold-weather.htm

Some species of yucca only live for a few decades, so yours might be nearing the end of its lifespan. It could also have a disease. You may want to remove the pups and plant them separately:
https://www.gardeningknowhow.com/ornamental/foliage/yucca/separating-and-repotting-yucca-offshoot-pups.htm

This article might help you:
https://www.gardeningknowhow.com/ornamental/foliage/yucca/yucca-turning-brown.htm

This can be quite simple to do. Even more so than most plants! Here is an article that will help: https://www.gardeningknowhow.com/ornamental/foliage/yucca/separating-and-repotting-yucca-offshoot-pups.htm

This is, most likely, a response to a lack of light, fertilizer, and possible overwatering. This will produce the symptoms that you are seeing.

This article will give you information on the proper care of these: https://www.gardeningknowhow.com/ornamental/foliage/yucca/growing-yucca-indoors.htm

Not likely, unless it was purposefully planted or harvested from near one. Being near some other very common houseplants, I would guess it to be a species of yucca, or cornpalm, or even a type of dracaena. They will all have very similar growth, and since this plant is young, it has no disinguising features to tell what it is.

Your local extension service will likely be able to help out here. This link will help you to find the closest one to you: https://www.gardeningknowhow.com/extension-search

This isn't a rubber plant. This is a type of yucca! It doesn't have the same care as a rubber plant, but CAN survive in such conditions. Hard pruning will bring it back to life, but you will also need to repot it while cutting off the bottom 1/3 of the root ball. Shake off the old soil and replace it with fresh soil. Water it in, letting any extra drain off. Give it an all purpose fertilizer after it starts to show new growth again.

This article will help: https://www.gardeningknowhow.com/ornamental/foliage/yucca/yucca-repotting-tips.htm