Thanks for sharing!
In Romans 10, I think the law means the whole Mosaic Law. Paul is talking about how to be saved, and not what applies to a person that is saved. We can read about that in other places (like Romans 8 and of course James 2). What does it mean to live by faith? A saved person is not to keep the Mosaic Law, but is to live a righteous life and not live in sin. If a person doesn't keep the commandments, doesn't that mean he/she livs in sin?
Romans 8
3 For what the Law could not do, weak as it was through the flesh, God did: sending His own Son in the likeness of sinful flesh and as an offering for sin, He condemned sin in the flesh, 4 so that the requirement of the Law might be fulfilled in us, who do not walk according to the flesh but according to the Spirit.
13 for if you are living according to the flesh, you must die; but if by the Spirit you are putting to death the deeds of the body, you will live. 14 For all who are being led by the Spirit of God, these are sons of God.