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.
Is it permissible for a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah Knows Best.
Should missed Sunnah prayer be made up?
Making up missed voluntary acts of worship is from Sunnah.
Does passing wind from the anus affect ritual purity?
Ablution is nullified by the passing of wind from the anus, but washing the anus is not required as wind leaves no impurity.