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Question 1:
He's being faithful to Himself as the God who cannot lie (Titus 1:2) and who has magnified His Word above His name (Psalm 138:2).
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In Romans 3:1-8, what is God being faithful towards?
The faithfulness of God is more about his constancy that his word is trustworthy and his promises absolute.
Even Einstein caught a part of this when he said that he believed in the God of Spinoza that made himself manifest in the harmony of nature.
Which words and which judging is referred to?
Romans 3:4 God forbid: yea, let God be true, but every man a liar; as it is written, That thou mightest be justified in thy sayings, and mightest overcome when thou art judged. - KJV
Romans 3:4 By no means! Let God be found true though every human being is false and a liar, as it is written, That You may be justified and shown to be upright in what You say, and prevail when You are judged [by sinful men]. - Amplified
Alternative translations can sometimes add a bit of clarity.
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The unfaithfulness of the Jews in no way hinders or nullifies God's promises to Abraham and his seed.
"What I am saying is this: the Law, which came four hundred and thirty years later, does not invalidate a covenant previously ratified by God, so as to nullify the promise." (Galatians 3:17 NASB)
Despite their unfaithfulness, God has confirmed and fulfilled the promises made to Abraham by sending Jesus, the promised offspring of Abraham (Romans 15:8) so that what was promised might be given to those who believe (Galatians 3:22), not to those who work the works of the law. Failure to keep the law does not negate God's faithfulness to his promise--the word of his oath--given to Abraham and his offspring.