Is it permissible for me to eat from the animal that I slaughtered for Allah to protect my family?
It is permissible to eat from the non-vowed animal sacrifice, and the person is rewarded based on the amount of meat that he had given to the poor. However, there is no evidence in Islamic Sharia indicating that slaughtering an animal protects one`s family, but it is a way for thanking Allah, The Almighty, for his grace.
Does the time of Fajr (dawn) prayer start after the first Athaan (call for prayer), or the second one?
All perfect praise be to Allah,The Lord of The Worlds The time of Fajr prayer starts after the second Adhan. And Allah Knows Best.
Do ear and nose drops break the fast?
Yes, ear and nose drops break the fast because both the nose and ears are open passages to the body cavity.
What is recommended for a Muslim to say on Laylat al-Qadr?
On Laylat al-Qadr, it is recommended for a Muslim to recite the supplication (du‘a) that the Prophet ﷺ taught Aisha (may Allah be pleased with her):
"O Allah, You are Most Forgiving, and You love forgiveness, so forgive me." [Narrated by Al-Tirmidhi]