What is the ruling on someone who eats or drinks while uncertain about the arrival of dawn, then later finds out that dawn had not yet broken?

If a person does this, their fast remains valid, as it is confirmed that they ate during the night. Similarly, if someone eats while uncertain and remains unsure whether they ate before or after dawn, their fast is still valid. This is based on the maxim of Sharia Law, which states: "Certainty is not removed by doubt." Certainty, here, is the presence of night, and the doubt concerns the arrival of dawn. Therefore, one relies on certainty and disregards doubt.

What is the ruling on the cessation of blood after (40) days from delivery, but later continued sporadically during two days of Ramadan?

Once postpartum bleeding (Nifas) ceases, and the woman is certain that it won`t reoccur, then she becomes ritually pure and so she is free to make Ghusl (purificatory bath), pray, and fast. If the bleeding reoccurs before fifteen days from its cessation, and before the end of (60) days after delivery, then the ruling on postpartum bleeding is effective, and her fasting and prayer are null and void, thus she must make up the fasting that she missed and not the prayer during those particular days.

What is the ruling on istinja' after urination, and is it done with water and soap or with water only?

Istinja' from urine and stool is obligatory. It is permissible to perform istinja' with water alone, or with toilet paper alone. The best way is with toilet paper then water. If one wishes to suffice with one of them, then water is better. And Allah the Almighty knows best.

What is the ruling on someone who fainted while fasting?