Is it permissible for a wife to refuse to go to bed with her husband (for sexual intercourse)?
It isn`t permissible for her to do so unless for a sound reason.
Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
Which is better for a traveler: fasting or breaking the fast?
Fasting is better, unless it causes hardship—in that case, breaking the fast is better.
How is the beginning of Ramadan determined?
1. Completing 30 days of Sha‘ban, or
2. Sighting the crescent moon after sunset on the 29th day of Sha‘ban.
It is Sunnah to search for the moon, and it is obligatory to follow the official authorities responsible for announcing it.