What is the ruling on mentioning Allah`s name upon slaughtering an animal?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is Sunnah for the slaughterer to say at the time of sacrificing the Udhiyah: (Bismillah - In the name of Allah); due to the saying of the Almighty: "So eat of that [meat] upon which the name of Allah has been mentioned" [Al-An'am/118]. It is not obligatory; if one leaves it out intentionally or forgetfully, the consumption of the meat remains permissible. And Allah the Almighty knows best.
What is the ruling on wiping the head during ablution from behind a barrier like a headscarf (hijab)?
The obligation in ablution is to wipe some of the head; it is not a condition to wipe all of it. As for one who has a turban or headscarf on their head, it is permissible for them to wipe over it after wiping a part of their head in any place. This is easily done at the front of the head. This means the woman begins by wiping the front of her head from under the headscarf, then completes the wiping to the back of the head from over the headscarf. If the woman wipes over the headscarf on her head and the moisture reaches the scalp or some hair within the boundaries of the head, it suffices for wiping the head. And Allah the Almighty knows best.
What is the ruling on bypassing a nearby mosque for a distant one?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If a distant mosque has a larger congregation (Jama‘ah) while the congregation in the nearby mosque is smaller, and the congregation in the nearby mosque is not adversely affected by the worshiper's absence, then it is better for him to pray in the distant mosque with the larger congregation. However, if the congregation in the nearby mosque would be affected by his absence—such as if he is its Imam, or if his presence encourages others to attend—then praying in the nearby mosque is better. This ensures that the congregation is established in two different locations within the community. This is based on the saying of the Prophet ﷺ: 'A man's prayer offered with another man is purer than his prayer which he offers alone, and his prayer with two men is purer than his prayer with one and if they are more (in number), it is more beloved to Allah, the Mighty the Majestic' (Narrated by Ahmad, Abu Dawood, and An-Nasa'i). And Allah the Exalted knows best.
Does smoking break the fast?
Yes, smoking breaks the fast because smoke particles intentionally enter the lungs, which are considered part of the body cavity (jauf).