Is the wife’s fasting valid if her postpartum bleeding stopped after two weeks, and she bathed and her husband had intercourse with her, then the blood reappeared only in the evening three days after that?

There is no minimum limit for lochia (post-natal bleeding); whenever a woman sees purity, she must perform ghusl (definition) (ritual bath) and pray. If the blood returns within the forty-day period, she reverts to being in a state of lochia. It is obligatory for her to perform ghusl, pray, and fast every time she sees purity. As for the intermittent purity, it is a valid state of purity, and she is not required to make up for any acts of worship she performed during it. Therefore, the wife's ghusl upon seeing purity and her fasting on that day are valid, and she is not required to make up for the fast she observed.