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 congratulating others on the arrival of Ramadan?
Congratulating others on the arrival of Ramadan is permissible.
If someone does it to express their love for worship and the blessings of Ramadan, and congratulates their fellow Muslim, they have done something good.
The Prophet ﷺ said: "Shall I not tell you something that, if you do it, you will love one another? Spread peace (Salam) among yourselves." [Narrated by Muslim]
Giving Salam is a prayer for peace and safety.
Is it permissible for a woman to observe voluntary fast without her husband's permission?
A woman is not permitted to observe a voluntary fast (nafl) while her husband is present without his permission.
Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.