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.

Should one who doesn`t perform prayer out of laziness make it up later, and how should he/she do so?

All perfect praise be to Allah,The Lord of The Worlds                                                                                                                                                              He/she is obliged to make up missed prayers by offering with each obligatory prayer another one, and if he/she offers two, then it is better. And Allah Knows Best.

If a father stops his daughter from getting married, is it permissible for her to conclude the marriage contract herself?

It is permissible for the father to stop his daughter from getting married if there was a lawful reason for that, and she isn`t allowed to conclude the marriage contract without her guardian. However, if her father denied her right in getting married for an unlawful reason, then she should go to court.

Does using a respiratory device (oxygen) affect the validity of fasting?