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.

Is a woman sinful if she fasts out of shyness from her family while menstruating or in postnatal bleeding?

What is the ruling on the ablution of one who washes his arms from the wrist to the elbows?

In the school of Imam al-Shafi'i (may Allah have mercy on him), washing the arms (hands) is achieved by washing the arms completely, from the fingertips to the elbows. Washing only the palms at the beginning is insufficient, as washing them at the beginning is a Sunnah, but after washing the face, it becomes obligatory (fard). The person performing ablution must wash his palms along with the arms after washing the face. If he does not wash his palms, his ablution is invalid and not correct. And Allah the Almighty knows best.

Is a woman`s prayer considered invalid if non-Mahrams (marriageable men) saw her offering it?

A woman`s prayer isn`t invalidated if non-Mahrams saw her offering it, but she had better pray in isolation.