Is it permissible for the young woman to turn the suitor down if she had no feelings for him?
Yes, it is permissible for her to do so.
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.
Is it obligatory for someone traveling by plane in the afternoon during Ramadan to fast?
Anyone who intends to travel after dawn must begin the day fasting and continue with the intention of completing their fast, as fasting was obligatory upon them before traveling.
However, if they experience unbearable hardship after starting their journey, they are permitted to break their fast due to that hardship, not merely because of travel. In such a case, they must make up for the missed fast later.
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.