Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
What is the ruling of Islamic Law on a fictitious marriage for the purpose of obtaining citizenship?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
There is no such thing in our noble sharīʿah as a "nominal" or "fictitious" marriage or divorce. Marriage and divorce are among the sacred ordinances of Allah, and it is not permissible to manipulate them or use them as a stratagem to obtain worldly gains.
The foundational purpose of a marriage contract is the permanence and continuity of the relationship between the spouses — to establish a family, and to bring forth righteous offspring. So sacred is this bond that Allah the Almighty Himself described it as a solemn covenant (mīthāq ghalīẓ), saying {what means}: "And if you wish to replace one wife with another and you have given one of them a great amount of wealth, do not take any of it back. Would you take it in injustice and manifest sin? And how could you take it while you have gone in unto each other and they have taken from you a solemn covenant?" [Al-Nisāʾ/ 20–21]
Accordingly, it is not permissible to resort to manipulation and deception in contracts that Allah, Mighty and Majestic, has described as a "solemn covenant" — all for the sake of material and worldly benefit. Marriage is built upon permanence and does not admit of a fixed time limit. If a time limit is stipulated in the contract, the contract is rendered invalid by the consensus of the jurists. Similarly, marriage is impermissible when there exists a mutual, concealed intention to limit its duration — even if no time limit is explicitly mentioned in the contract — for this constitutes a form of unlawful circumvention of the sharīʿah. This is to say nothing of the lying and deception that such conduct involves, the prohibition of which needs no elaboration. Lying, deception, and fraud for the purpose of obtaining worldly gains are among the gravest of sins.
If, however, the marriage contract is first concluded in a valid sharʿī manner and then registered civilly, it is sound and fully valid. And Allah the Almighty knows best.
Is a woman's prayer performed while following an Imam whose prayer is being broadcasted via the television valid, and does she receive the reward of congregational prayer?
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 (Iqtida’) is that the Imam and the follower must be in the same location. Therefore, the prayer of one who follows an Imam whose prayer is being broadcasted 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.
Is it permissible for me to eat from the animal that I slaughtered for Allah to protect my family?
It is permissible to eat from the non-vowed animal sacrifice, and the person is rewarded based on the amount of meat that he had given to the poor. However, there is no evidence in Islamic Sharia indicating that slaughtering an animal protects one`s family, but it is a way for thanking Allah, The Almighty, for his grace.