What is the ruling on congratulating others on the arrival of Ramadan?
Congratulating others on the arrival of Ramadan is permissible.
If someone does it to express their love for worship and the blessings of Ramadan, and congratulates their fellow Muslim, they have done something good.
The Prophet ﷺ said: "Shall I not tell you something that, if you do it, you will love one another? Spread peace (Salam) among yourselves." [Narrated by Muslim]
Giving Salam is a prayer for peace and safety.
Is it permissible to slaughter one animal as a sacrifice and an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)?
It is impermissible to do so since each of them is slaughtered for a different reason.
Is it permissible to pay the Fitr Zakah (obligatory charity) of Ramadan on behalf of a dead person?
The Fitr Zakah of Ramadhaan isn`t due on one who had passed away before the sunset of the last day of Ramadan. And Allah Knows Best.
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.