What is the ruling on swearing on the Holy Quran and breaking that oath?
It is impermissible to swear on the Holy Quran in vain, and it is also impermissible to subject it to such an act since breaking the oath after swearing on the Quran entails an expiation.
What is the semi-circular structure attached to the Holy Kabah?
The semi-circular structure attached to the Holy Kabah is Hijr Al-Kabah (is a low wall originally part of the Kabah) and passing behind it is an obligation while making Tawaf because it is a part of the Holy Kabah. 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.
What is the ruling of Islamic Law on wearing energy stones?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
There is no objection to a woman adorning herself with precious and semi-precious stones — such as ruby, carnelian, or the like — so long as these are stones that women customarily wear as adornment.
As for what are known as "energy stones," if they are used with the intention of seeking remedy and healing, then such matters are governed by experimentation and scientific study — which either establishes that they have a tangible effect or does not — and all of this operates by the permission and will of Allah, Glorified and Exalted. If studies or practical experience do establish that such stones carry a beneficial effect upon human health, then there is no objection to using them. They are, after all, part of Allah's creation, much like medicinal substances extracted from plants or derived from other created things — provided that the Muslim does not believe that the stone itself is the source of benefit or harm. It is nothing more than a means among the many means that Allah has placed in this world, and the reality of all affairs belongs to Allah alone. And Allah the Almighty knows best.