What is the ruling of Islamic Law on sitting between the two prostrations, and what is the ruling on the dhikr recited during it?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
Sitting between the two prostrations (al-jalsah bayna al-sajdatayn) is one of the pillars (arkān) of the prayer, while the dhikr recited during it is Sunnah according to the Shāfi'ī scholars. It is recommended (mustahabb) to say what was narrated from Ibn 'Abbās (may Allah be pleased with him), who said: "The Messenger of Allah (peace and blessings be upon him) used to say between the two prostrations in the night prayer: 'Rabbi ighfir lī, warhamnī, wajburnī, warzuqnī, warfa'nī' (My Lord, forgive me, have mercy on me, make good my deficiencies, provide for me, and raise me)." If one were to say a different supplication instead, such as "Rabbi ighfir lī" (My Lord, forgive me), the prayer would still be valid.
If the worshipper omits this dhikr between the two prostrations, whether intentionally or out of forgetfulness, their prayer remains valid and nothing is required of them, though they miss the reward of following the Sunnah. Leaving it out does not necessitate the prostration of forgetfulness (sujūd al-sahw).
It is stated in Hāshiyat al-Bājūrī 'alā Sharḥ Ibn Qāsim 'alā Matn Abī Shujā' (Vol.1/P.298): "The eleventh — i.e., of the eighteen pillars — his statement: 'sitting between the two prostrations,' meaning even in a supererogatory (nafl) prayer... his statement: 'with the supplication that has been narrated concerning it,' meaning: 'Rabbi ighfir lī, warhamnī, wajburnī, warfa'nī, warzuqnī, wahdinī, wa 'āfinī' (My Lord, forgive me, have mercy on me, make good my deficiencies, raise me, provide for me, guide me, and grant me well-being). Al-Ghazālī added: 'wa'fu 'annī' (and pardon me). Al-Mutawallī also added: 'Rabbi hab lī qalban taqiyyan, naqiyyan min al-shirk, bariyyan lā kāfiran wa lā shaqiyyan' (My Lord, grant me a heart that is God-fearing, pure from associating partners with You, innocent, neither disbelieving nor wretched)."And Allah, the Most High, knows best.
Is the prayer of a woman who is led by an Imam via T.V. permissible?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions. Amongst the conditions for the validity of prayer is that both the Imam and those led by him must be in the same place. Thus, the prayer of the person who is being led by a televised Imam is invalid unless he/she was with him in the same mosque. And Allah Knows Best.
What is the ruling on shaving the head of the newborn?
It is desirable to shave the head of the newborn on the seventh day from delivery, and the weight of his/her hair is given in gold , or silver as charity.
I hired a private tutor for my son through an academy that sends teachers [to families] and takes a percentage [of their pay]. At the start of the [new] school year, I arranged directly with that same teacher, without the academy's knowledge. What is the ruling on this?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The ruling on this matter depends on knowing the specific terms of the agreement and contract concluded with the academy. If the agreement stipulates that no arrangement may be made with any of the students except through the academy itself, then it is not permissible for you to breach the terms of this contract, based on the words of our master, the Messenger of Allah ﷺ: "Muslims are bound by their conditions." (Related by al-Bukhārī)
However, if the agreement pertains only to teaching a specific subject, and the agreement concludes once that subject is finished, then there is no objection to arranging with the teacher to teach other subjects after the contract period has ended, outside of the academy.
Whatever the case maybe, the teacher must uphold the terms of his contract with the academy. And Allah, the Exalted, knows best.