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The “Works” you refer to in Romans and Galatians have nothing whatsoever to do with “the Law of Moses.” It is the false laws of men forced upon the Jews by the Pharisees. They were what Yeshua invoked the “woes” on the Pharisees and scribes for in Matthew 23.
If you read Acts 28, you will see that it is the “Law of Moses” that Paul preached throughout his ministry. (also see 1Corinthians 11 where he praises the Corinthians for keeping those “ordinances.”)
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Yes, they do and it's been shown here over and over again.