Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
What is the ruling on using a patch to suppress hunger or a nicotine patch while fasting?
Fasting is a great act of worship and one of the pillars of Islam. If people knew the immense reward of Ramadan, they would wish for the whole year to be Ramadan.
Whoever eats Suhoor and breaks their fast according to the Sunnah will not experience extreme hardship, making such patches unnecessary.
However, using these patches does not break the fast because they are not a source of nourishment and do not enter the body cavity (jauf) through an open passage.
How should I deal with the whispers of the devil with regard to ablution and purity?
Whispers in ablution are from the devil, and so you should take refuge in Allah from the devil`s evil suggestions that aim to distort the religion. Thus, once an organ is completely pure, don`t question its purity since having whispers doesn`t mean that the purity is invalid as it has already been established.
Is it permissible for a woman to shake hands with her brother-in-law?
It is forbidden for the woman to shake hands with her brother-in-law because he isn`t a Mahram (unmarriageable) of hers.