When is it Sunnah to slaughter the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah for the 'aqīqah to be slaughtered on the seventh day from the birth of the newborn. According to the sounder position, the day of birth itself is counted as the first of the seven days. Thus, for example, if the child is born on a Saturday, the 'aqīqah is to be slaughtered on the following Friday. If the child is born at night, the count begins from the day that follows. And Allah Almighty knows best.
Which is better for a traveler: fasting or breaking the fast?
Fasting is better, unless it causes hardship—in that case, breaking the fast is better.
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.
What is the ruling on performing istinja' before every ablution?
Istinja' is not from the conditions for the validity of ablution. It is only obligatory for prayer when there is impurity from urine or stool on the private part, or if there is fear of the impurity spreading to the body or clothing. And Allah the Almighty knows best.