What is the ruling on speaking while relieving oneself?
It is disliked for one relieving himself to speak while doing so, except out of necessity. And Allah the Almighty 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 should someone do if they fasted for 30 days in their country, then traveled to a place where people are still fasting?
If a person completes 30 days of fasting in their country and then travels to another country where people are still fasting, they should continue fasting with them until they observe Eid. Even if they have already completed 30 days, he/she should abstain from eating and drinking and join the people of that country because he/she has now become part of that community.
What type of illness that permits breaking the fast in Ramadan?
It is an illness that, if one fasts, there is a fear it may lead to their death or cause unbearable hardship.