Regarding making du’a while washing the limbs during ablution, we would like to quote for you the fatwa issued by the Standing Committee for Islamic Research and Ifta’ in Saudi Arabia which states:
There is no proof that the Prophet (peace and blessings be upon him) made any du`a during wudu’ whilst washing or wiping his limbs. Any from of du`a mentioned in this regard is innovated and has no basis.
What is known from Islamic sources is that one should say “Bismillah il-Rahman il-Rahim” at the beginning, and after finishing one should recite the Shahaadatayn and say, “Allaahumma-j’alni min al-tawwaabeen waj’alni min al-mutatahhireen (O Allah, make me one of those who are oft-repentant and make me one of those who purify themselves).”