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 a person in a state of major impurity (junub) walking or eating before performing the ritual bath?
It is from the Sunnah for a Muslim to hasten to perform the ritual bath for major impurity. However, if he delays it, he does not sin provided he does not miss the prayer. It is permissible for the junub to walk, eat, drink, and sleep. It is recommended for him to perform ablution before these actions to reduce the state of impurity, although the best is for him to perform the ritual bath. And Allah the Almighty knows best.
What is the ruling of islamic law on statutory (legal) interest awarded by a court?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is permissible for a person in whose favor a judge has awarded statutory (legal) interest to deduct the actual litigation costs incurred in filing and prosecuting the lawsuit from these interest funds.
Any remaining balance beyond those actual expenses must be returned to the party upon whom the payment was imposed, provided that party is a specific individual. If, however, the paying party is a public entity or state institution, the remaining amount should be spent on the general public interests of Muslims—such as schools, mosques, roads, and similar public utilities shared by the community—or given in charity (Sadaqah) to the poor and needy. And Allah Almighty knows best.
What is the ruling on performing the obligatory prayer immediately after the commencement of the Adhan?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is permissible to perform the obligatory prayer (Fard) immediately after the commencement of the prayer time. As the Adhan (call to prayer) serves as a sign that the time has entered, it is permissible to pray as soon as the Adhan begins. However, it is recommended (Mustahabb) for whoever hears the Mu’adhin to repeat what he says. If the Adhan occurs while one is already engaged in prayer, he should repeat the words of the Mu’adhin after he has completed his prayer. And Allah the Exalted knows best.