What is the ruling of Islamic Law on the colored discharges that appear one or two days before the menstrual cycle?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Colored discharges carry the same Islamic ruling as blood, whether they appear at the beginning or the end of the menstrual period. This remains true even if the discharge is intermittent—appearing for some days and stopping for others before returning—provided that the total duration does not exceed fifteen days nor fall short of a day and a night (24 hours). This is because the minimum duration of menstruation (Hayd) is one day and a night, while its maximum duration is fifteen days. Furthermore, the minimum period of purity (Tuhr) between two menstrual cycles is fifteen days, and there is no maximum limit for it. And Allah the Exalted 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.
Is it permissible to give multiple mudds (portions) of fidyah to a single person?
Yes, it is permissible to give multiple mudd of fidyah to a single person, because each day of fasting is considered an independent act of worship.
What is the ruling on one who slept while firmly seated on the ground, regarding nullification of ablution?
The default ruling regarding sleep is that it nullifies ablution. An exception to this is one who slept while firmly seated on the ground; his ablution is not nullified by sleep if he wakes up while still firmly seated on the ground. And Allah the Almighty knows best.