Yes, it does and it's a fascinating study. The ten commandments fall outside of any covenant. They are actually the essence, the written definition, of what love toward God and others should manifest as.
Amen!
This is incorrect. The ten commandments are referred to in both the Old and New Testament as the "tablets of the covenant", clearly in the context of the covenant with Isreal.
Jesus didn't come to destroy the law, but to fulfill it, and He did fulfill it. He also came to set us free from the law. Paul, in Romans clearly establishes that we died to the law, and uses the tenth commandment as his example.
Those who cling to the ten commandments do so in ignorance of New Testament commandments.