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 a woman who takes medication to delay menstruation for fasting?
If a woman takes medication (to delay menstrual period) and does not experience menstruation, her fast is valid. However, she is not advised to do so unless there is a necessity.
If the medication harms her, even potentially, it is forbidden (haram) for her to take it.
What are the Sunnahs and etiquettes related to the slaughtering of an animal?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
1-The animal should not be terrified or frightened before it is slaughtered.
2-An animal should not be slaughtered in front of other animals.
3-It is recommended to offer water to the animal before it is slaughtered.
4-The knife must be sharpened before the slaughter to ensure that the esophagus, trachea, and jugular veins are severed as quickly and cleanly as possible. This is based on the Prophet’s (peace be upon him) saying: "Verily, Allah has prescribed Ihsan (excellence/proficiency) in all things. So, if you kill, kill well; and if you slaughter, slaughter well. Let each one of you sharpen his blade and let him spare the animal unnecessary suffering." [Narrated by Muslim].
5-One must not begin skinning or butchering the animal until its death has been fully confirmed.
6-Cows and Sheep: It is best to slaughter them while they are lying on their left side, facing the Qiblah. The right hind leg should be left untied so the animal can move it, which helps it remain more comfortable during its final moments. Unlike other livestock, it is preferred to perform Nahr (slaughtering by a swift stab at the base of the neck) while the camel is standing, with its left knee tied. And Allah the Almighty knows best.
Is it permissible for a pious Muslim woman to stay with her husband who had quit praying out of laziness?
Quitting prayer is one of the major grave sins that come after disbelieving in Allah, but the wife of such a person isn`t considered divorced, rather, she should exert all her efforts in order to bring him back to the way of Islam. However, if his sin is likely to lure her from the way of Islam, then she had better separate from him by lawful means such as Mokhal`aa (When a wife pays a compensation for her husband in return for divorcing her). Moreover, if she exercises patience, and remains steadfast on her faith, then there is no harm in doing that.