What type of illness that permits breaking the fast in Ramadan?
It is an illness that, if one fasts, there is a fear it may lead to their death or cause unbearable hardship.
Is it incumbent on a father to cover the marriage costs of his son if the latter couldn`t afford them?
The son should seek the help of his relatives in order to convince his father to do the aforesaid, and the father should make sure that his son doesn`t commit fornication through helping him to get married, and Allah will reward him for doing so.
What is the ruling of Islamic Law on supplicating with other than the transmitted (Ma'thur) supplications in prayer?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible to supplicate (make du'a) during the prayer for anything from the affairs of religion or worldly life, and the prayer is not invalidated by doing so.
Shaykh al-Islam, the Imam an-Nawawi, may Allah have mercy on him, says: "Our madhhab [i.e., the Shafi'i madhhab] holds that it is permissible for a person to supplicate during it [the prayer] with anything that is permissible to supplicate with outside the prayer, from the affairs of religion or worldly life. He may say: 'O Allah, grant me wholesome sustenance, offspring, a house, and a beautiful young wife' — describing her; or: 'O Allah, free so-and-so from prison,' or 'destroy so-and-so,' and other such things — and none of this invalidates his prayer according to us. And this is also the view of Malik, ath-Thawri, Abu Thawr, and Ishaq." [Al-Majmu', Vol.3/P.454]. And Allah, the Exalted, knows best.
What is the ruling of Islamic Law on performing prayer on the upper floors of al-Masjid al-Ḥarām?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Facing the actual structure of the Ka‘bah (‘ayn al-Ka‘bah) is one of the conditions for the validity of the prayer. The scholars have clarified what is meant by "the actual structure of the Ka‘bah."
Imam ash-Sharwānī (raḥimahullāh) said: "What is meant by its ‘ayn (actual structure) is its physical body, or the airspace directly aligned with it — if the person praying is not inside it. But if he is inside it, then the airspace alone does not suffice; rather, the actual physical structure must be faced, such that even if he faces a projecting part of it measuring roughly two-thirds of a dhirā‘ (cubit) or more, this would be sufficient." [Ḥāshiyat ash-Sharwānī ‘alā Tuḥfat al-Muḥtāj, Vol.1/P.484]
Sheikh al-Qulyūbī (raḥimahullāh) said: "Unlike one who prays outside it — i.e., outside the Ka‘bah — for him the airspace (directly above it) suffices, even if he is higher than it, or even if he is at the location where it (hypothetically) has been demolished." [Ḥāshiyat al-Qulyūbī ‘alā Sharḥ al-Minhāj, Vol.1/P.154]
Accordingly, the prayer is valid on the upper floors of al-Masjid al-Ḥarām, even though these floors are higher than the roof of the Ka‘bah itself. And Allah, the Exalted, knows best.