Start of Prayer's Time
One may say their prayer as soon as they become confident that it is time for prayer. 

Adhān Timetables
By referring to the timetables and mass media, if one gets certain that the shar‘ī time has set in, it is enough; otherwise, they should wait till they are certain. 

Moonlit Nights
There is no difference between nights, moonlit or otherwise, as regards fajr arrival, the time of morning obligatory prayer, and the obligatory time of abstinence for fasting, though it would be good to observe caution in this regard.

Time for 'Asr Prayer
The time for 'asr prayer ends at sunset.

To Say the Second Prayer First
A person who has performed 'asr prayer before 'noon' one or ‘ishā’ prayer before maghrib one by mistake or by negligence and he remembered only when he had completed the prayer, then it is correct. But if he did so intentionally, it is invalid.