Is what my wife sees after her period stops due to birth control pills considered istihada (vaginal bleeding outside of menstruation) or a regular period, and is she permitted to fast?

If a wife sees blood after fifteen days or more since her previous menstruation ceased, then it is menstrual blood, and it is considered a second menstruation. In this case, it is impermissible for her to fast or pray, by scholarly consensus. However, if it is determined that she is experiencing istihada (non-menstrual vaginal bleeding), then she has the rulings of those who are pure: she may pray and fast. She must perform ablution for every prayer after its time has begun, while taking precautions (to prevent blood from staining her clothes).