Is ablution invalidated when blood comes out of the nose, or a wound?
Blood coming out of the nose, or a wound does not invalidate ablution, but it is preferable to make ablution as a way out of the scholars disagreement in this regard.
What is the Islamic ruling on one who was unable to fast and then regained the ability?
He is not required to make up the fast (Qada) even if he becomes capable of it; whether he regained the ability to fast after paying the fidya (feeding a needy person for each day of missed fasting) or before it, because he was liable for paying it in the first place, so it remains binding upon him. However, if he delayed paying it beyond the first year, nothing is required of him due to the delay. If he is unable to pay it, it does not remain as a debt upon him. And Allah the Exalted 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 permissible for the guardian to give Sadaqa (voluntary charity) from the money of the orphans?
It is impermissible for the guardian to donate from the money of the orphans because he is entrusted with the safekeeping of that money, and is prohibited from donating it.