How should I deal with the whispers of the devil with regard to ablution and purity?
Whispers in ablution are from the devil, and so you should take refuge in Allah from the devil`s evil suggestions that aim to distort the religion. Thus, once an organ is completely pure, don`t question its purity since having whispers doesn`t mean that the purity is invalid as it has already been established.
What is the ruling on swearing an oath by the Prophet ﷺ, and does such an oath take effect according to Imām Aḥmad ibn Ḥanbal, requiring expiation upon its breach?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
Swearing an oath by a created being is disliked (makrūh) in our Shāfiʿī school. Shaykh al-Islām Imām al-Nawawī, may Allah have mercy upon him, states: "Swearing by a created being is disliked — such as swearing by the Prophet, the Kaʿbah, Jibrīl, the Companions, or the Prophet's family. Al-Shāfiʿī, may Allah have mercy upon him, said: 'I fear that swearing by other than Allah the Almighty may constitute an act of disobedience.' The scholars of the school explained this to mean: that is, something forbidden and sinful — indicating that he had some hesitation in the matter. Al-Imām stated: the established position of the school is that it is categorically not forbidden, but rather disliked. Furthermore, whoever swears by a created being, his oath does not take effect and no expiation (kaffārah) is required if he breaks it." [Rawḍat al-Ṭālibīn wa ʿUmdat al-Muftīn, Vol. 11/P.6]
According to the Ḥanbalī school, however, expiation becomes obligatory upon one who swears by our master the Prophet ﷺ and then breaks his oath. Imām al-Bahūtī al-Ḥanbalī, may Allah have mercy upon him, states: "No expiation is required for swearing by other than Allah the Almighty, even if the oath is broken — because expiation was made obligatory for swearing by Allah and His attributes, out of reverence for His names, and nothing else is equal to Him in this regard... except in the case of swearing by our Prophet Muḥammad ﷺ, for expiation becomes obligatory when one swears by him and then breaks the oath. This was explicitly stated in the narration of Abū Ṭālib, because he is one of the two conditions of the two testimonies of faith by which a disbeliever becomes a Muslim. Ibn ʿAqīl held the view that swearing by any of the other prophets, peace and blessings be upon them all, carries the same ruling." [Sharḥ Muntahā al-Irādāt, Vol. 3/P.441]. And Allah the Almighty knows best.
Does using a gargling medicine break the fast?
If the medicine reaches the body cavity (jauf), the fast is invalidated. However, if it does not enter the body cavity, the fast remains valid.
Therefore, it is advisable to avoid using it during the day in Ramadan.
Is washing the private part after urinating (Istinjaa`) a condition, and is it done with water and soap, or with water only?
Istinjaa` is obligatory for removing impurity, and it can be done with toilet paper, or a stone, or water. It is preferable to do Istinjaa` first with paper, or stone, or the like, then to wash the private part with water until making sure that the impurity has been removed. Using soap is not a condition, but there is no harm in doing so provided that it is washed off with water. It is also permissible to use either water, or paper if impurity is removed by any.