Is wiping over the feet with water instead of washing them in wudu sufficient due to skin cracking, pain, and the foul odor caused by water?

Wiping the feet during ablution (wudu') instead of washing them is not sufficient, because their obligation is to be washed. If washing the cracked area (of the foot) causes harm, then wiping it is permissible. The prayers that were performed with ablution in which the entire foot was wiped must be repeated, due to the invalidity of that ablution.

As for the ruling on a wound in the purification organs, it progresses from washing if it does not harm it, to wiping if washing harms it but wiping does not, or to tayammum (dry ablution) if both washing and wiping harm it, or to wiping over the covering if it is covered with a bandage or similar.