Is the saying that the 'awrah (private parts that must be covered) extends from the navel to the middle of the thigh correct, supported by the narration of the Prophet, may Allah’s prayers and peace be upon him, uncovering his thigh upon the entry of Abu Bakr and Umar, and then lowering his garment upon the entry of Uthman? And is the mujtahid (one who exercises independent reasoning in Islamic law) rewarded for this opinion?

The aforementioned Hadith in the question was narrated by Muslim from Aisha (may Allah be pleased with her) that the Prophet (peace be upon him) was reclining when Abu Bakr and Umar (may Allah be pleased with them) entered while he was in that state. Then Uthman (may Allah be pleased with him) entered, and the Prophet sat up and adjusted his clothes.

In one narration, he said: "Should I not be shy of a man whom the angels are shy of?"

This Hadith cannot be used as proof for the permissibility of uncovering the thighs. Imam Al-Nawawi was uncertain whether what was uncovered were the shins or the thighs. Authentic and explicit evidence has been reported stating that the thigh is part of the 'awrah (private parts).

As for Ijtihad (independent juristic reasoning), it is only valid from someone who has reached its rank, which is attained only through diligence, hard work, vast knowledge, and comprehensive understanding of various branches of knowledge. If he performs Ijtihad and is correct, he receives two rewards; if he errs, he receives one reward. This applies to one who possesses the tools of Ijtihad, is familiar with the principles, and is knowledgeable of the various forms of analogy. However, one who is not qualified for Ijtihad is presumptuous and is not excused for error.