What's your question? Ask

Light and temperature can sometimes cause a Christmas cactus to change color, though normally that is from a less dominate color, like white, to a more dominate color, like pink. It can also happen if you get a genetic mutation, also known as a sport but that would occur on only a single stem.

It sounds like yours, since it was blooming one color and is now blooming another, something has changed with the light and temperature and this is causing the flowers to change as well.

As long as the pot is big enough, they will be fine together. You can use both the existing soil and new soil.

Near the end of this article, there are directions for growing the seeds:
https://aggie-horticulture.tamu.edu/plantanswers/publications/cactus/growingcactus/index.html

They bloom more on a schedule based on dormancy, water and light than time of year. It sounds like they were possibly inadvertently put into a dormant state (this can happen if the plant is left unwatered for a period of time) and received the required amount of dark hours at that same time. When normal care resumed, the Christmas cactus went into blooming stage.

It has root rot. It is hard to say how well it will recover. This article will help:
https://www.gardeningknowhow.com/plant-problems/disease/treating-root-rot-gardening-tips-for-housplants.htm

I would get some starts from the plant, just in case it does not make it. This article will help with that:
https://www.gardeningknowhow.com/ornamental/cacti-succulents/christmas-cactus/how-to-propagate-and-plant-christmas-cactus.htm

Christmas cactus and snake plants have similar water and light needs, so they will be fine planted together.

I believe the plant you have is a Elephant Ear Philodendron or Selloum Philodendron. You can repot it if you like, though they are pretty forgiving of a crowed pot. Do not trim those viney things at the base, they are aerial roots. I would recommend providing something for these roots to cling to, like a pole of some kind.