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 fasting only on Friday, Saturday, or Sunday?
In voluntary fasting (nafl), it is disliked (makruh) to fast only on Friday, Saturday, or Sunday.
However:
● If one fasts a day before or after Friday, then that is permissible.
● The same applies to Saturday and Sunday—fasting them along with another day removes the dislike.
● Fasting all three days (Friday, Saturday, and Sunday) together is not disliked.
If any of these days coincide with a recommended fasting day, such as Arafah or Ashura, then fasting it alone is not disliked.
Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
Is it permissible for one to shake hands with his uncle`s daughter?
No, it isn`t because he is a non-Mahram (Marriageable) to her.