No, the covenant is with man (it does not make sense that God makes a covenant with Himself - the point is that God Himself has met the conditions of the covenant He has made with man). .
No, you are teaching conditional covenant righteousness - justification by works. It makes perfect sense that God makes a covenant with Himself as three divine persons IF substitutionary atonement is its basis in Christ. The whole point is that God accomplished "in Christ" the substitute what cannot be accomplished "in Adam."
God told Adam that if he ate of the fruit he would die (Covenant with man),
That is not a "covenant" that is a decree made by God without any consent made by man whatsoever.
God told Abraham that he would bless him and through him redemption would come (Covenant with man),
That is the unconditional "everlasting covenant" obtained "in Christ" and performed by Christ. However, his covenant with Abraham conditioned on circumcision is another story.
God told Moses (and Israel) to do those things and live (Covenant with man),
Half truth! Israel agreed and said they would (other half of truth, thus an actual covenant between two parties).
These are commands not a covenant! The everlasting covenant secured the demands among his elect as that was the covenant responsibility of the Holy Spirit.and Jesus said "repent and believe", "believe and live",
that God loved the world in this way - He sent his only Son that whoever believed would have everlasting life (Covenant with man)
That is not a covenant with man but the declaration of the everlasting covenant