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There are a few reasons that this can happen. The most common is that there is too much flouridation in the water for these plants. You will have to switch to distilled or RO water. This will more than likely eliminate your problem.

This article will give you more information: https://www.gardeningknowhow.com/houseplants/ti-plant/growing-hawaiian-ti-plant-indoors.htm

Just wipe it with peroxide. By now, whatever could infect it has already gotten in. Usually, this will not be a big deal, though. IT will heal on its own, as long as it hasn't been "ringed" of a section of bark. That is, if there is continuity of bark from bottom to top.

If it is just an axe wedge, it will likely heal. Can you include a photo? This can help me to see the damage and help you a little better.

The stones should not sink unless the plant is being overwatered. They will, usually sit on top. If they do start getting buried in, you may look towards watering with bottom watering pots, or watering in such a way as to not disturb the soil.

Furthermore, have care when placing stones on top. This will make it more difficult to tell when the soil is dry down to 2 or 3 inches. You should not water again until it is completely dry down to this depth. You may have to remove the stones in an area to check every few days or so.

This article will give you proper care of these plants: https://www.gardeningknowhow.com/houseplants/ti-plant/growing-hawaiian-ti-plant-indoors.htm

It may be too late to resurrect this plant. Whatever killed it, possibly crown rot, you don't want to spread to any other plants, so I would discard this and start over with a new healthy one.

This appears to be a Cordyline. I would not replant deeper into the soil This will cause more problems than it is worth. They will do this in very humid environments, and will often lose the adventitious roots once the humidity breaks. These can grow quite tall, and will only, usually, have growth on the top.

Here is an article that will help with general Cordyline care, though the cultivar that you have is a little more cold tolerant: https://www.gardeningknowhow.com/houseplants/ti-plant/growing-ti-plants-outdoors.htm

Pruning these plants will be very straightforward. You can prune them to any height that you would like, since they will grow new tops.

This article will be for its closest relative, Cordyline australis, which has the same care requirements: https://www.gardeningknowhow.com/houseplants/ti-plant/red-star-dracaena-care.htm