Is the father a Mahram (Non-marriageable) to his son`s mother-in-law?
The father is a non-Mahram (Marriageable) to his son`s mother-in-law, so it is impermissible for them to look at each other, or to have a seclusion (Khalwah).
What are the categories of the livestock permissible for Udhiyah?
Praise be to Allah, and peace and blessings be upon the Messenger of Allah.
The Udhiyah (sacrificial offering) is not valid except from Al-An’am (livestock), which are: camels, cattle, and sheep/goats. Allah the Almighty says {what means}: "And for every nation We have appointed a rite [of sacrifice] that they may mention the name of Allah over what He has provided for them of beast-livestock." [Al-Hajj/34]
The best of them are camels, then cattle, then sheep/goats. A sacrifice of a camel or a cow avails for seven people. Jabir (may Allah be pleased with him) said: "We sacrificed with the Messenger of Allah (peace and blessings be upon him) in the year of Al-Hudaybiyah a camel for seven and a cow for seven." [Narrated by Muslim] And Allah the Almighty knows best.
What is the ruling on fasting?
Fasting in Ramadan is an individual obligation (Fard ‘Ayn) upon every mature, sane Muslim who is capable of fasting.
Fasting can also be recommended (Mustahabb), such as voluntary fasting on Mondays and Thursdays, fasting on the Day of Arafah for those not performing Hajj, and fasting on Ashura.
Fasting can be prohibited (Haram), such as fasting on the two Eid days, the Day of Doubt (Yawm al-Shakk), and the Days of Tashreeq.
Some types of fasting are disliked (Makruh), such as singling out Friday or Saturday for fasting without a specific reason and fasting on the Day of Arafah for a pilgrim.
Is it permissible to pay the Zakah (obligatory charity) for settling the debt of a deceased relative?
It is impermissible to pay the Zakah for settling the debt of the deceased since Zakah is paid to eligible recipients who are alive. As for the debts of the deceased, they are to be settled from the estate before dividing it amongst the heirs, but if the deceased didn`t leave an estate, then it is desirable for his/her heirs to settle those debts if they can afford them. And Allah Knows Best.