What are the conditions for the validity of the slaughtering process according to Sharia?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Regarding the Sharia-mandated conditions for the validity of the slaughtering process (Adh-Dhabh), they are as follows:
The Identity of the Slaughterer: The person performing the slaughter must be either a Muslim or from the People of the Book (Christian or Jewish).
The Required Cuts: Both the trachea (windpipe/breathing passage) and the esophagus (food passage) must be completely severed.
Stability of Life: The animal must possess stable life at the start of the slaughtering process. This is identified by clear signs, such as vigorous movement or the forceful gushing of blood after the throat and esophagus are cut.
The Tool of Slaughter: The tool used must be sharp, capable of cutting or piercing by its edge and not by its sheer weight or blunt force.
And Allah the Almighty knows best.
Is bleeding that lasts for nine or ten days considered menstruation (Hayd)?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
If the duration of the bleeding does not exceed fifteen days, then all of it is considered menstruation (Hayd), even if the regular cycle ('Adah) has changed. And Allah the Exalted knows best.
Is it permissible to divide one mudd of fidyah between two people?
No, it is not permissible to divide one mudd between two people, because it would not count as a full meal for either of them.
Is it permissible for a wife to give her money to her family as a charity, or a gift without asking her husband, or seeking his consent?
The wife has the right to give her money as a charity, or a gift to her family, or to other people after consulting her husband out of respect, and this is the meaning of treating on footing of kindness and equity. Therefore, if he wanted to stop her from helping her family, then there is no harm in not telling him.