If a woman in nifas sees that she has become pure before 40 days are over, then she should do ghusl and pray and fast, and her husband may have intercourse with her.

It is haram for a Muslim woman to continue fasting when she is menstruating. If she gets her period while fasting, her fast is spoiled, even if the blood comes a moment before sunset, and she has to make that up if it was an obligatory fast.

Any bleeding that resumes after the period is over is not menstrual blood. So you can pray, fast, do tawaf or any other acts of worship.

If a woman had an abortion before 80 days of pregnancy, then the blood she passes is not the blood of Nifas which does not stop her from praying and fasting, but she has to do Wudu for each prayer. If the abortion took place after the soul was breathed into the foetus, then the blood is definitely Nifas and she cannot pray or fast.