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 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.
What is the ruling on giving the expiation of an oath (Kaffarat al-Yamin) to a charity that feeds the poor?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is allowed for a Muslim to appoint a proxy (agent) to distribute the expiation (Kaffarah) on their behalf. Our jurists have explicitly stated the permissibility of delegation (Tawkil) in the distribution of Zakat, Kaffarah, and vows (Nadr).
It is stated in Mughni al-Muhtaj (Vol.3/P.237): 'One has the right to pay the Zakat of their wealth personally... and they also have the right to delegate it.' And Allah the Exalted knows best.
What is the ruling on the prayer of the individual following the imam whose prayer is broadcasted via television?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Among the conditions for the validity of following an Imam (Sihhat al-Iqtida’) is that the Imam and the follower (Ma’mum) must be in the same location. Therefore, the prayer of one who follows an Imam whose prayer is being broadcast via television from a distant location is not valid. However, if the follower is with the Imam in the same mosque, the prayer is valid. And Allah the Exalted knows best.