What is the ruling on eating or drinking during the first Adhan?
It is permissible to eat and drink during the first Adhan because it takes place before the break of dawn. The purpose of this Adhan is to notify Muslims of the approaching dawn so they can prepare to stop eating when they hear the second Adhan.
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.
If a woman becomes pure from menstruation shortly after Fajr in Ramadan, what is required of her?
If a woman becomes pure (from menstrual period) after Fajr, even shortly after, it is recommended (but not obligatory) for her to refrain from eating and drinking for the rest of the day. However, she must make up for that day after Ramadan.
She will be rewarded for both refraining from eating (imsak) and making up the fast (qada) since she was menstruating for part of the day.
Some online stores offer a discount on a customer's first purchase — what is the ruling on creating a new account each time a customer makes a purchase in order to obtain that discount?
All praise is due to Allah, and peace and blessings be upon our master the Messenger of Allah ﷺ.
It is obligatory upon a Muslim to uphold honesty in both his words and his actions. Allah the Almighty says {what means}: "O you who have believed, do not betray Allah and the Messenger or betray your trusts while you know." [Al-Anfāl/ 27] And He says {what means}: "O you who have believed, fear Allah and be with the truthful." [Al-Tawbah/ 119]. And the Messenger of Allah ﷺ said: "Whoever deceives us is not of us." (Reported by al-Bukhārī.)
As for creating a new account for the same buyer, the terms and conditions of the website must be observed and respected. If doing so violates those terms, it is not permissible. And Allah the Almighty knows best.