Must a person refrain from eating for the rest of the day if they break a fast of a vow (nadhr) or a make up fast (qada)?
Whoever observes a vowed fast (nadhr) or a makeup fast (qada) is prohibited from breaking it without a valid excuse. If they break it without a legitimate reason, they are sinful.
However, they are not required to refrain from eating for the rest of the day, because such restraint is only required out of respect for the month of Ramadan, not for other types of fasting.
Does the fast become invalid if water from rinsing the mouth reaches the stomach while performing ablution?
If water reaches the stomach without the fasting person exceeding normal rinsing or being excessive, their fast remains valid.
However, if they exceed the normal practice or exaggerate in rinsing, causing water to enter the stomach, their fast is invalid.
This is because excessiveness in rinsing is prohibited for a fasting person, as the Prophetﷺ said: "Exaggerate inhaling water during ablution, except when you are fasting." [Narrated by the Four Imams]
Transgression (Ta‘addi) refers to rinsing the mouth more than three times, while exaggeration (Mubalaghah) includes gargling, drawing water deep into the nasal passages, or filling the mouth with water in an unusual manner.
What is the ruling of Islam on swearing by Allah without intending to take an actual oath?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If someone swears by Allah without intending to take an actual oath, and without the firm resolve to bind themselves to it, then there is no sin or expiation (Kaffarah) required of them. Allah the Exalted says {what means}: 'God will not call you to account for thoughtlessness in your oaths, but for the intention in your hearts; and He is Oft-forgiving, Most Forbearing.' [Al-Baqarah/225]. However, a Muslim should avoid swearing oaths excessively so that their tongue does not become accustomed to it. Allah the Exalted says {what means}: 'And make not God’s (name) an excuse in your oaths against doing good, or acting rightly, or making peace between persons; for God is One Who heareth and knoweth all things.
' [Al-Baqarah/224]. And Allah the Exalted knows best."
What is the ruling on wiping the white area behind the ears instead of wiping the head?
The obligation in ablution is to wipe some of the head; it is not a condition to wipe all of it. Wiping the white area behind the ears suffices for that. And Allah the almighty knows best.