Deuteronomy seems to be part of a Jewish religious history collection, continuing with Joshua, Judges, Samuel and Kings. Kings ends in the middle of the 1st temple period. That's how it is dated.
At that time, the Covenant was still physically existing, Salomon had a temple being built around it. It didn't contain the Torah, but the Decalogue (10 Commandments).
Every people has a language. All people around spoke Semitic languages; the Mt Sinai inscriptions are very close to Hebrew. Of course, every language changes in 500 years, compare the King James Bible. Similar to the Kingjamesish English, which was still used for any sacred texts until the 1960s, the Hebrew of the time of the first temple became the reference language in Judaism and decoupled from the spoken language.
The name Deuteronomy is Greek, given another 500 years later, and it speaks of the perception by that time only.
Compared to Genesis,Exodus, Leviticus and Numbers, it shows a redactional unification, best seen in the notorious usage of the first person for God, which is highly artificial, and wants to underline it's claim to be the direct Word of God.
The other books don't do that, and scientists found out that Gen and Ex show traces that they have been written on the base of older written accounts. Ex, Lv,Nb are much closer to the original sources than Dtn, which essentially draws from the same sources but adds some more recent laws, although it may have been compiled earlier