When Ukrainians or Russians move to a new house, they let the cat go into the house first. The cat can go around and sit somewhere. They put the bed where the cat sits down. The cat never chooses the place with the negative energy.

It's even better when you see the thing where it gets you to translate this into Ukrainian because you get to see the message straight away.

yep

This is a good question. The answer is straightforward, if not entirely simple.

This sentence translates literally to "The house is there, where the cat is," but that doesn't make sense in English. In English we don't need the adverb (there) before the relative pronoun (where), so we eliminate the "there." Ukrainian requires it. If we took it out of the original, we would end up with Дім де кіт, which would mean something like "House where cat." Because Ukrainian doesn't use copulas (for our purposes, "be" verbs), this sentence doesn't make sense without that там to guide us.

In English, structures like this are called free relative clauses and they are quite ordinary: I like what you did; She ate what she wanted; We can hear what you're saying. These sentences can't exist in Ukrainian without antecedents. For example, Мені подобається те, що ти зробила (I like that, which you did = I like what you did); Вона їла те, що хотіла (She ate that, which [she] wanted = She ate what she wanted); Ми чуємо те, що ви говорите (We hear that, which you are saying = We [can] hear what you're saying).

"The cat is home" would be "Кіт удома" if you mean "The cat is at home", and "Кіт — це дім" if you actually mean "The cat is (my) home".

"The cat is at the house" would be "Кіт біля дому" (in this case "at" means "nearby" right?)

I tried "The cat is home ". It's not a possible translation. Maybe someone else will attempt the other one.

Your home does not necessarily have to be a house. And some house is not necessarily your home.

Home -> дім

House -> дім, будинок