Then God spoke to Noah and to his sons with him
God was already speaking to them. This phrase marks a change in what God was going to speak about. AT: "God continued speaking to Noah and his sons" or "Then God went on to say"
As for me
This phrase is used in English to mark the change from God talking about what Noah and his sons must do to talking about what God would do.
confirm my covenant with you
"make a covenant between you and me." See how you translated this in Genesis 6:18.