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.
During a flight from Amman to the UAE, while we were flying over Saudi Arabia, the captain announced that it was time to break our fast, coinciding with the exact time of sunset. After I had broken my fast with my first date, the captain apologized for the earlier announcement and clarified that the correct time would be in 20 minutes. Am I required to continue fasting on that day?
Whosoever break his fast at teh very first announcement to make up the missed day of Ramadan, since Allah, The Most Exalted, Said (What means): "then complete your fast Till the night appears" [Al-Baqara/187]. And Allah Knows Best.
Is a woman`s neck an Awrah (private part)?
All Perfect Praise is due to The Lord of The Worlds.
It is an Awrah, and it is forbidden for her to reveal it before non-Mahrams (Marriageable men). And Allah Knows Best.
What is the ruling on uncovering the eyes while wearing a Khimar?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
According to Sharia, a woman`s clothing shouldn`t be attractive so as to prevent sedition. However, it is better for a woman to be on the safe side and avoid such clothes. And Allah The Almighty Knows Best.