The identical actions of the Lord and the Angel of the Lord show they are the same Being. The God known by Abraham, Isaac, Jacob, and Moses was Jesus Christ.
Hebrews 1-2 establish Christ's superiority over angels, but notably do not mention the Angel of the Lord. Instead, the author handles the Angel differently.
The Eight Day (or Last Great Day) has little written about it, but the patterns of Scripture reveal much about the abundance of this holy day.