Translation:She has four coats but I do not have any coat.
cóta happens to be one of those words where the genitive singular is the same as the nominative singular. But other examples of ceithre on Duolingo (ceithre lítear and ceithre chat use nouns where the nominative singular and genitive singular are different, and they use the nominative, not the genitive. (There are other examples using troigh but that's one of a small number of exceptions that do use plurals when counting).
In the Caighdeán, the personal numbers use the genitive plural, e.g. ceathrar ban (“four of women”), but the regular numbers use the nominative singular, e.g. ceithre dheoir (“four tear”), rather than ceithre *dheoire (“four of tear”), ceithre *dheora (“four tears”) or ceithre *dheor (“four of tears”).
I'm not entirely sure that I understand your question, but the word order is different in Irish and English - basic English sentences are subject-verb-object, and Irish sentences are verb-subject-object. "she" and "I" are the subjects of the two basic sentences that are joined together with "and", so "she" and "I" go at the start of these sections.
To further complicate matters, the Irish phrase that is used to translate the English verb "to have" puts the subject at the end, combined with the preposition "ag", so you have "tá ... aici" for "she has ..." (where "aici" is derived from "ag sí") and "níl ... agam" for "I don't have ..." (where "agam" is derived from "ag mé").