What should the one performing the slaughter say at the time of slaughtering the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah to say the following supplication at the time of slaughtering the 'aqīqah:
"Bismillāhi wallāhu Akbar, Allāhumma laka wa ilayka, hādhihi 'aqīqatu fulān."
("In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of [the child's name].")
This is based on what al-Bayhaqī narrated in Al-Sunan al-Kubrā (Vol.9/P.511), that the Prophet ﷺ said: "Slaughter it in his name and say: In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of so-and-so."
And Allah Almighty knows best.
What is the ruling of Islamic Law on kissing while fasting?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
It is prohibitively disliked (makrūh taḥrīman) for a husband to engage in foreplay with or kiss his wife during the daylight hours of Ramaḍān if doing so stirs his desire. If pre-seminal fluid (madhī) is released as a result, the fast is not invalidated; however, if seminal fluid (manī) is released, the fast is broken.
Imām al-Khaṭīb al-Sharbīnī, may Allah have mercy upon him, stated: "It is prohibitively disliked to kiss — whether on the mouth or elsewhere — for one whose desire is stirred, whether man or woman, to the extent that he fears it may lead to intercourse or ejaculation. Embracing, touching, and similar acts without a barrier carry the same ruling as kissing in this regard, because such acts expose the act of worship to being corrupted — and as the two Ṣaḥīḥs record: 'Whoever circles around a protected boundary is liable to fall into it.'"
He further added: "It is preferable for one whose desire is not stirred — even if he is a young man — to refrain from such acts as well, so as to close the door entirely. For he may believe his desire has not been aroused when in fact it has. Moreover, it is Sunnah for the fasting person to abstain from all desires without exception." — Summarised with minor adaptation from [Mughnī al-Muḥtāj]. And Allah the Almighty knows best.
Is it permissible for a menstruating woman to recite the Quran from the computer without actually touching the Quran?
It is not permissible for a woman in her menstrual period, or in postpartum to recite the Quran, even by heart, or without actually touching the Quran itself. Recitation itself is what is prohibited on her regardless of how it is done. However, it is permissible for her to surf through the Quran by her eyes, or to recall it in her head without uttering the words. There is no harm for her to look at the Quranic verses on the computer without touching it, or to utter the words as this is called looking not reciting or reading.
Is it permissible for a woman who has become pure before the end of forty days of confinement to perform different acts of worship? and is it lawful for her husband to have sex with her?
Once postpartum bleeding ceases and she is certain that it won`t happen again, she becomes pure, and so she should perform Ghusl (ritual bath), pray, and fast. She can also have sex with her husband even before the end of (40) days because the minimum of postpartum bleeding is a moment, and the maximum is (60) days. However, the postpartum bleeding for the majority of women is (40) days, but this does not apply to rest of them.