What is the ruling on men wearing rings (those made of silver and of other metals, such as iron), and are there conditions for men wearing rings?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is sunnah for men to wear a silver ring on the right hand, following the practice of the Prophet (peace and blessings be upon him). It is reported in Ṣaḥīḥ al-Bukhārī, on the authority of Anas ibn Mālik (may Allah be pleased with him), that the Messenger of Allah (peace and blessings be upon him) took a silver ring and had “Muḥammad Rasūl Allāh” engraved on it. He said: “I have taken a ring of silver and had ‘Muḥammad Rasūl Allāh’ engraved on it, so let no one engrave the like of its engraving.”
It is a condition that the silver ring not exceed the size customary in the local norm (ʿurf). If it does, that is extravagance (isrāf). A ring made of a metal other than silver, such as iron or copper, is permissible to wear without disapproval (karāhah), except gold, which is forbidden (ḥarām) for a man to wear.
It is stated in Mughnī al-Muḥtāj (Vol.1/p.586): “It is permissible, without disapproval, to wear a ring of iron or lead. It is sunnah for a man to wear a silver ring on the little finger of his right or left hand. Wearing it on the right is better, and it is permissible on the left, and on both together.”
It is also stated in Mughnī al-Muḥtāj (Vol.2/p.97): “It is lawful for him, that is, the man, and likewise the khunthā (person of indeterminate sex), indeed all the more so, to wear a ring of silver, by consensus (ijmāʿ), because the Prophet (peace and blessings be upon him) took a ring of silver, narrated by the two Shaykhs (al-Bukhārī and Muslim). Wearing it is in fact sunnah, whether on the right or the left, though the right is better according to the sound position, as stated in the chapter on clothing in al-Rawḍah… The Shāfiʿī jurists did not specify the permitted size of the ring, and they probably relied on custom (ʿurf), that is, the custom of that country and the habit of people of his standing in it. Whatever exceeds that is extravagance, as they said regarding a woman’s anklet. This is the reliable position (al-muʿtamad).” And Allah Almighty knows best.
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.
Can a woman leading other women in Tarawih prayer recite aloud?
Yes, a woman leading other women in Tarawih prayer is allowed to recite aloud, as long as no non-mahram (other than unmarriageable kin) men can hear her.
What is the ruling on the intention of fasting, where is its place, and when is its time?
The intention is a pillar of acts of worship; it is essential, and worship is not valid without it.
Its place is in the heart, and verbalizing it is recommended so that the tongue reminds the heart. Its meaning is to be determined to abstain from nullifiers of fasting during the upcoming day with the intention of worship and obedience to Allah Almighty. This meaning is naturally present in every Muslim on every night of Ramadan, so there is no need for obsessive doubts. If one says, "I intend to fast tomorrow for the sake of Allah," it removes any doubts.
Its time is from after sunset until before the true dawn.