What is the ruling on forming an intention for each second wash during ablution (wudu'), such as intending the second wash of the face to complete the obligatory (fard) act, and intending the second wash of the feet solely for the Sunnah?

The obligation when performing ablution (wudu') is to have the intention (niyyah) of removing ritual impurity (hadath) at its beginning. There is no need to renew the intention for each washing; the initial intention suffices. If, with the second washing of the face, you intend to complete the washing, and with the second washing of the feet, you intend virtue and Sunnah, this does not cause harm or affect the validity of the ablution. However, it is easier to suffice with the intention of removing ritual impurity at the very beginning.