Which takes precedence: the 'aqīqah or the uḍḥiyyah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The 'aqīqah is an act of worship through which a servant draws closer to Allah the Almighty in gratitude for the blessing of a newborn child. It is a confirmed Sunnah for those who are financially capable, and Allah does not burden any soul beyond what it can bear.
However, the uḍḥiyyah takes precedence, as it is a confirmed Sunnah established from the Prophet ﷺ through stronger and more numerous narrations — indeed, the Ḥanafī scholars hold it to be obligatory. Furthermore, its time is narrow and limited, expiring with the passing of the days of Eid, whereas the 'aqīqah may be delayed until one becomes financially capable of performing it.
And Allah Almighty knows best.
What is the ruling on Jumu‘ah (Friday) prayer for a traveler, and what are the conditions for it to be waived from him?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Jumu‘ah (Friday) prayer is not obligatory upon a traveler, whether on a long or short journey, provided that — according to the Shāfi‘ī school — he departs from his place of residence before the time for Fajr prayer begins, and that he does not intend to stay in the place he travels to for four days or more, excluding the day of arrival and the day of departure. If he intends to stay longer than that, he may not make use of the travel concession simply by arriving in that town. If he begins his journey after the adhān for Fajr has already been called, then Jumu‘ah prayer remains obligatory upon him, whether in his own town or in any town where Jumu‘ah is being held.
It is stated in Bushrā al-Karīm (Vol.1/p.383), from the books of the Shāfi‘ī school: "Jumu‘ah [prayer] is not obligatory upon a traveler on a permissible journey, whether long or short, if he departs from his place of residence before Fajr."
A "short journey" refers to travel covering a distance shorter than that of a long journey — that is, less than (81 km). The traveler begins to be entitled to travel concessions once he passes beyond the built-up limits of his town. And Allah, the Exalted, knows best.
What is the ruling on praying behind a disliked Imam?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is mildly disliked (Makruh Tanzihan) for a man—other than the permanent designated Imam (Imam Ratib)—to lead people in prayer if the majority of them dislike him due to a religiously blameworthy reason (Amr Madhmum Shar‘an), such as associating with open sinners (Fussaq), for example. As for the followers who dislike him, the prayer behind him is not disliked for them. However, if less than the majority dislike him, or if the majority dislike him for a reason that is not religiously blameworthy, then his leading the prayer is not disliked. And Allah the Exalted knows best.
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.