What exactly, did Moshe transcribe?
Rashi: He transcribed the Torah from Bereishis until here, and the Mitzvos that Yisrael were cpmmmanded at Marah. 1
Ramban (in Pasuk 1), Rashbam and Seforno: The Aseres ha'Dibros and all the Mitzvos in Mishaptim. 2
When did Moshe arise and build a Mizbe'ach?
Rashi: On the morning of the fifth of Sivan. 1
Ramban: On the morning of the seventh of Sivan. 2
What is the significance of the twelve Matzeivos that Moshe built?
Rashbam: It was a testimony that all twelve tribes agreed to enter into the covenant with Hashem.
Refer to 15:27:1:1*.
How could Moshe build Matzeivos, whenm based on the Pasuk in Re'ei, Chazal state that after the time of the Avos, the Matzeivah became hated in the eyes of Hashem?