Is the Hadith "Fight them until you defeat them" authentic, and is it permissible to act upon it if it leads to a violation of Sharia?

We do not know of any origin for this hadith. What is prescribed in trade is that it should be based on honesty and trustworthiness, and be free from deception, fraud, and violations of Islamic law. This is because merchants will be resurrected on the Day of Judgment as wicked, except for those who feared Allah, acted righteously, and were truthful. The Prophet, peace and blessings be upon him, forbade deception, for "whoever deceives is not of me." He also forbade najsh, which is increasing the price of a commodity without intending to buy it, and talaqqi al-rukban (meeting riders outside the city to buy their goods before they reach the market), and a city dweller selling on behalf of a Bedouin, and tasriyah al-ghanam (tying the udders of sheep to make them appear to have more milk).