What are the regulations for sighting the crescent moon to determine the beginning of lunar months, how many hours after the conjunction can the crescent moon be sighted, and does the determination of months rely on the Shar'i (Islamic) astronomical calculation or the Chinese one?

The beginning of Ramadan is determined by one of two things: completing thirty days of Sha'ban, or sighting the crescent moon with the naked eye by two trustworthy witnesses, or by widespread sighting (mustafid), or by one trustworthy witness according to the more preponderant opinion. This sighting is what obligates fasting. The crescent moon usually starts thin then grows bigger. The noble verse was revealed concerning this: (They ask you about the new moons. Say: they are fixed times for the people) [2:189]. The beginning of the months of Sha'ban and Rajab is determined in the same way, by sighting or by completing thirty days of the previous month. The legal sighting is with the naked eye and is not established by astronomical calculations. As for the Chinese moon, if it relies on astronomical calculations, then the legal sighting is not established by it. But if what is meant is the visible crescent moon in the sky of China, then it is like any other; it is relied upon there, or upon the sighting of a nearby country if there is no difference in horizons.