Is it Sunnah to cook the meat of the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah not to distribute the meat of the 'aqīqah raw. Rather, it is recommended to cook it with something sweet — such as raisins or honey — as a good omen and expression of hope for the sweetness of the newborn's character and conduct throughout their life. And Allah Almighty knows best.
Is it a condition that a woman should untie her locks while making Ghusl (ritual bath)?
Ghusl from Janabah (ritual impurity), or menstruation obligates that water reaches the roots of the hair in order for the Ghusl to be valid, but if it doesn`t, then hair locks must be untied for water to reach them, and for Ghusl to become valid.
Is it enough to say Tasbeeh (Saying Subhaana Rabbiya Al-‘Atheem during Rukoo`, and saying Subhaana Rabbiya Al-A‘laa during Sujood ) once, or twice during Rukoo`(Bowing in prayer) and Sujood (Prostration)?
All perfect praise be to Allah, The Lord of The Worlds Yes, saying Tasbeeh once during Rukoo` and Sujood is enough, provided that the worshiper`s attentiveness of the heart isn`t undermined during each. As regards the recompense, it depends on the number of Tasbeeh. And Allah Knows Best.
A man wishes to offer more than one uḍḥiyah (sacrificial offering), and intends by these sacrifices "on behalf of everyone whom Allah and His Messenger love." Is this intention valid?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The uḍḥiyah (sacrificial offering) is not valid with this intention, because if the sacrificial animal is from sheep or goats, it suffices for one person only; and if it is from cattle or camels, it suffices for seven persons.
However, one may sacrifice it on his own behalf, and then gift the equivalent of its reward to whomever he wishes.
Imam ar-Ramlī (raḥimahullāh) says: "Ash-Shāfi‘ī (raḍiyallāhu ‘anh) said: It is within the vastness of Allah's bounty, the Exalted, that He rewards the one giving charity as well. From this, the scholars of the madhhab said: it is recommended for a person to intend the charity on behalf of his parents, for example — for Allah, the Exalted, will reward them, without this diminishing his own reward in any way." He then relates, as the relied-upon position, the permissibility of saying: "O Allah, convey the reward of what I have recited specifically to so-and-so, and to the Muslims generally." Az-Zarkashī said: "For reward varies in degree — its highest form is what one designates specifically, and its lowest form is what one dedicates generally [alongside others]." [End of quote from Nihāyat al-Muḥtāj]. And Allah, the Exalted, knows best.