What is the ruling on using eye drops while fasting?
Eye drops do not break the fast, even if the taste reaches the throat, because the eye is not an open passage to the body cavity.
What is the ruling on praying in congregation at the mosque?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Congregational prayer (Salat al-Jama‘ah) is a communal obligation (Fard Kifayah) for resident men regarding the performance of the prescribed (obligatory) prayers. For men, praying in congregation at the mosque is better than praying elsewhere, such as at home. On the authority of Abdullah bin Umar, the Messenger of Allah ﷺ said: 'Prayer in congregation is twenty-seven degrees more excellent than the prayer of a person alone' (Reported by Bukhari & Muslim). Furthermore, on the authority of Abu Hurayrah, the Messenger of Allah ﷺ said: 'Shall I not tell you that by which Allah erases sins and raises ranks?' They said, 'Of course, O Messenger of Allah.' He said: 'Performing wudu thoroughly despite difficulties, taking many steps toward the mosques, and waiting for the next prayer after the prayer; that is your Ribat (steadfastness)' (Narrated by Muslim).
As for a woman, her praying in congregation at home is better for her than in the mosque, according to the saying of our Master the Prophet ﷺ: 'Do not prevent your women from attending the mosques, but their homes are better for them' (Narrated by Abu Dawood). Young boys should be encouraged to attend the mosques and congregational prayers so they may become accustomed to them. And Allah the Exalted knows best.
What is the ruling on the cessation of blood after (40) days from delivery, but later continued sporadically during two days of Ramadan?
Once postpartum bleeding (Nifas) ceases, and the woman is certain that it won`t reoccur, then she becomes ritually pure and so she is free to make Ghusl (purificatory bath), pray, and fast. If the bleeding reoccurs before fifteen days from its cessation, and before the end of (60) days after delivery, then the ruling on postpartum bleeding is effective, and her fasting and prayer are null and void, thus she must make up the fasting that she missed and not the prayer during those particular days.
Is the one offering the sacrifice liable if its meat spoils?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
If the meat (of the sacrifice) spoils due to the negligence of the one offering the sacrifice in preserving it, or due to improper storage, then he is liable to compensate for the portion due to the poor (which is estimated as half a kilogram of meat). If the sacrifice was a vowed (mandatory) one, then he is liable for all of it.
However, if he was not negligent, then there is no liability upon him, because its ruling is the ruling of a trust (like an item left in someone's care). And Allah Almighty knows best.