The people's of the 12 World's draw their lineage to various earthly civilizations.The magical 'events' that brought them to there new home's would also often bring along their belongings and settlements, even entire villages. However, assuming that a certain settlement was of, say, Victorian Britain, was transplanted to some mysterious new world, how well would it be able to keep its culture and technological knowledge, and how could I make doing so easier?
You might be able to keep the culture for a single generation, the one of the initial settlers, but it will be changing starting from the next one.
Culture is strongly dependent on the people, the location and the interaction those people have. Therefore changing the interactions and the location you are changing the culture.
Same for technological knowledge: it will change, gaining and losing content depending on the specific instances of their daily life. For example if they don't have horses, any horse-related aspect of their technology will be gone. Look at our world: taking care of a horse or donkey was common knowledge just 80 years ago, nowadays it's knowledge of a small group.
Technology is highly dependent on the supply chain. A technology that can use local materials can be transplanted to a new area and be kept. For example, pottery spreads quickly because it uses local clays. Cell phones are highly dependent on the current supply chain and would not be usable on another world without importing huge amounts of supplies. Imports will be hugely expensive and prohibitive for nearly anyone. A museum might have a cell phone to show people what is done elsewhere.
Victorian Britain had a lot of technology: steam engines, steel working, automated looms for weaving, coal mining, ship building, brick making, construction, beer brewing, Scotch distilling, barrel making, to name a few. Most of these were built upon centuries of saved up knowledge kept by specialized people. Not every village had knowledge of how to do more than a few of these. The empire traded around the world so that a village didn't need to know how to make most stuff. They traded for the stuff they didn't know how to make.
So, if you were thinking of people taking technology and moving to another planet, the technology they can use would have to be stuff that can use whatever materials are locally available. Think of stone tools, pottery, and any plant materials that might be there. If you took only a village, you are taking at random a very select bit of technology knowledge.
The process of moving a group of people to a new location is by nature, a bottleneck on the transmission of knowledge. A lot of knowledge will be lost when the first generation of people die as most of what they know will not fit the new location and it will not be passed on to the next generation.
Attempts to preserve the old ways will doom the village to a death as most of the old ways will not work well or will be extremely expensive.
The best you can hope for is to catch a rare general purpose genius who knows how to teach learning skills to the next generation. Instead of keeping the old technology, through trial and error, they will learn and develop the technology that works best in the new environment.
firstly you would need a minimum viable population. https://www.britannica.com/science/minimum-viable-population. If you have too few people then you will get too many problems with genetic diseases.
Culture is always changing. It is influenced by the environment and other cultures. so by removing it from that environment it would immediately change at least a little. If you transplant a large enough area then some people may not notice the change as quickly and would therefore preserve more of their culture.
Technology is a something more easily kept when transplanted. You would need enough knowledgeable people/library's supporting skill full individuals able to create every necessity. And have every resource available to them that they are used to using when making those products. This is more of a problem in modern cultures.
Now for the case of Victorian England.
The whole country is getting rich or has been getting rich from the exploitation of the America's, Ireland, India, and China. Suddenly removing those resources and income would be devastating to those English people's. Inevitably changing their culture to reflect the increased poverty. Effectively the Victorian culture is dependent on those other ones existing.