Absolutely. Just read Galatians 3 for the proper understanding of "Seed" being Jesus Christ and the fact that all those found to be in Christ are the true sons of Abraham and, therefore, heirs of the promises.
Well, now, see, I have to take this as an obtuse "no". Christ did indeed fulfill one promise of the Abrahamic Covenant, but there was more to the Covenant. The New Covenant did not cancel the Old Covenant, and a Gentile Church did not replace a Jewish Nation. Supersessionism is completely without Biblical basis. Replacement theology, not eschatology, is the real disagreement between Dispensationalism and Covenant Doctrine. And "Covenant" doctrine does, indeed, teach that God has broken His covenants.
If the Church is heir to the promises of the Old Covenant, then why is the Church not heir to the obligations of the Old Covenant?
Because the promise did not change, and the obligations have been fulfilled in Jesus Christ.
What is the plain language interpretation of “In speaking of a new covenant, he makes the first one obsolete. And what is becoming obsolete and growing old is ready to vanish away. “