Q 2: Is it from the articles of faith to believe that Adam was the first prophet as was pointed out by Allah's saying in the Qur'an:
Then Adam received from his Lord Words. And his Lord pardoned him (accepted his repentance).
? What are the clear proofs of the prophethood of Adam?
A:
The first messenger to be sent was Nuh (Noah) as was mentioned in the Hadith of the intercession reported in the Two Sahih (authentic) Books of Hadith (i.e. Al-Bukhari and Muslim).As to Adam, it was said that he was a prophet, and therefore he was the first prophet. This is proved by the Ayah (verse) stated in the question and by the saying of Allah (Exalted be He):
And indeed We made a covenant with Adam before, but he forgot, and We found on his part no firm will-power.
There are many Ayahs that denote Allah's inspiration to him. However, we do not have an explicit and authentic proof that confirms that he is a messenger (peace be upon him).May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.