Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
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.
What is the ruling on wiping the head during ablution from behind a barrier like a headscarf (hijab)?
The obligation in ablution is to wipe some of the head; it is not a condition to wipe all of it. As for one who has a turban or headscarf on their head, it is permissible for them to wipe over it after wiping a part of their head in any place. This is easily done at the front of the head. This means the woman begins by wiping the front of her head from under the headscarf, then completes the wiping to the back of the head from over the headscarf. If the woman wipes over the headscarf on her head and the moisture reaches the scalp or some hair within the boundaries of the head, it suffices for wiping the head. And Allah the Almighty knows best.
How should a person who is afflicted with continued major ritual impurity (incontinence of urine, bleeding outside the monthly period) perform ablution?
Such a person should make ablution for every prayer after its due time and after removing impurities from their body and outfit, and should place a fresh diaper whenever needed so as for the impurity not to spread out. They should also perform prayer immediately even if incontinence of urine continued, and should repeat the aforementioned for every obligatory prayer, then perform optional prayer as much as they want.