The Danish word comes from Old Norse dœgn, ultimately a derivation from Proto-Germanic dōgaz ‘daily’. (If one is familiar with comparative Germanic linguistics, the long vowel in the Old Norse form speaks against any borrowing from Latin diurnāta). Meanwhile, Latin diurnāta is a derivation from dies ‘day’, unrelated to the Germanic word.
If you are curious about where words come from, the English-language Wiktionary often has etymologies in its entries for words, and for the Nordic languages they are usually pretty up-to-date in terms of the scholarly state of the art.
Oh yeah that’s a good one. Both Zeus and Jupiter are cognates of Dyus Pter (Sky Father) of old Indo European mythology. They just took different parts of that name.
If you are curious about where words come from, the English-language Wiktionary often has etymologies in its entries for words, and for the Nordic languages they are usually pretty up-to-date in terms of the scholarly state of the art.