What is the amount of the Fitr Zakah (obligatory charity) of Ramadan?
The Fitr Zakah of Ramadhaan is a Sa` (2500 grams) from what the people of that country or state eat the most. And Allah Knows Best.
Who is responsible for performing the aqiqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The one upon whom the 'aqīqah is incumbent is whoever is obligated to financially maintain the newborn — whether the father, paternal grandfather, or mother. It is to be performed from their own wealth, not from the wealth of the newborn child.
As for one upon whom the financial maintenance of the newborn is not obligatory, they may not perform the 'aqīqah except with the permission of the one upon whom it is obligatory — namely, the father. And Allah Almighty knows best.
Is "Bismillāhir-Raḥmānir-Raḥīm" a verse (āyah) of Sūrat al-Fātiḥah?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The basmalah ("Bismillāhir-Raḥmānir-Raḥīm") is, without question, a verse (āyah) of the Noble Qur'an, and according to the Shāfi‘ī school, it constitutes a verse of Sūrat al-Fātiḥah itself. Al-Fātiḥah is a pillar of the prayer, and it consists of seven verses, of which the basmalah is one. The prayer is not valid without reciting it, nor if any of the Fātiḥah's verses, letters, or shaddahs (consonant doublings) are omitted or altered.
It is stated in Bushrā al-Karīm (Vol.1/p.202), from the books of the Shāfi‘ī school: "The basmalah is a complete verse of it [i.e., of al-Fātiḥah] in practice — and it suffices, for this to be established, that there be strong probability (ẓann), especially given that this has come very close to certainty (yaqīn), due to the consensus (ijmā‘) of the Companions on its inclusion in the muṣ-ḥaf [the written text of the Qur'an] in its script, despite their extreme diligence in excluding from it anything that did not genuinely belong to it — to the point that they even [carefully regulated] its diacritical dots and vowel markings." And Allah, the Exalted, knows best.
Is it incumbent on the fiancée to obey her fiancé?
When the woman settles in her husband`s house, it is incumbent on him to provide for her and it is incumbent on her to obey him. Before that, and if the marriage contract had been concluded, then she is lawfully his wife and thus she should abide by custom in treating him, but if the marriage contract hadn`t been concluded, then she should treat him as a non-Mahram (Marriageable).