1)
Why did Hashem need to say "Anochi Hashem ... asher Hotzeisicha me'Eretz Mitzrayim ... ?
1.
Oznayim la'Torah: To impress upon Yisrael that, as opposed to the nations of earlier generations, who believed that the land, the sea and the desert each had different gods, Hashem in the desert was the same G-d who took them out of Egypt, and there would be no change of jurisdiction. 1
1
See Oznayim la'Torah, whio elaborates.
2)
What is the meaning of "mi'Beis Avadim"?
1.
Refer to Sh'mos 20:2:6:1-5.