Was I correct in shunning the atheists who mock the Prophet, peace and blessings be upon him, and the Book of Allah, and who spread false hadiths, or should I have debated them? And if debating them is obligatory, can I send you the page link so that scholars may debate them?

If you possess knowledge and the ability to refute the falsehoods of atheists, and you see benefit in doing so, then respond to them. However, if you do not see significant benefit or do not have sufficient knowledge, then turn away from them and do not waste your time on their websites and pages, for Allah Almighty says: "And when you see those who engage in [offensive] discourse concerning Our verses, then turn away from them until they enter into another conversation. And if Satan should cause you to forget, then do not remain after the remembrance with the wrongdoing people." (Al-An'am: 68). Engaging in [offensive] discourse concerning Allah's verses means speaking what contradicts the truth and promoting false propositions.