What is the ruling on water present on the floor of a toilet/bathroom?
The default ruling is the purity of this water present on the bathroom floor. If one is certain or strongly suspects its impurity, then one washes whatever part of the body or clothing this impure water has touched. If one doubts its impurity, the default is purity, and we do not rule it impure based on mere doubt. And Allah the Almighty knows best.
What is the virtue of performing ‘Umrah in Ramadan?
Ibn ‘Abbas narrated: "When the Prophet ﷺ returned from his Hajj, he said to Umm Sinan Al-Ansariyyah: ‘What prevented you from performing Hajj?’ She replied: ‘Abu So-and-so (referring to her husband) had two camels—he performed Hajj on one of them, and the other was used to irrigate our land.’ The Prophet ﷺ then said: ‘Performing ‘Umrah in Ramadan is equivalent to Hajj with me.’" [Narrated by Al-Bukhari]
The Prophet ﷺ also said: "An ‘Umrah in Ramadan is equivalent to a Hajj." [Narrated by Al-Tirmidhi]
For those who miss the opportunity to perform ‘Umrah in Ramadan, there are many other ways to earn great rewards. One of them is praying Fajr in congregation, then remaining in the mosque remembering Allah until sunrise, and praying two rak‘ahs.
The Prophet ﷺ said: "Whoever prays Fajr in congregation, then sits remembering Allah until the sun rises, and then prays two rak‘ahs, will receive the reward of a complete Hajj and ‘Umrah—complete, complete, complete." [Narrated by Al-Tirmidhi]
Is it valid for the 'aqīqah to be performed using the newborn child's own wealth?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is not permissible for the guardian to perform the 'aqīqah using the newborn child's own wealth, because the 'aqīqah is a voluntary act of giving (tabarru'), and a guardian is prohibited from making voluntary expenditures from the child's wealth. Should he do so, he becomes financially liable for what he spent. And Allah Almighty knows best.
Are school exams a valid excuse for breaking the fast in Ramadan?
School and university exams are not considered a valid excuse for breaking the fast, as most students take their exams while fasting without experiencing extreme hardship. Fasting does not conflict with exam preparation, and a Muslim seeks strength in obedience to Allah for both worldly and spiritual matters.