Is it permissible to perform the Asr prayer based on the measurement of shadows, and what is the ruling concerning previous prayers performed before that, and what is the ruling concerning the Dhuhr prayer if it is performed between three and four o'clock, given that the Dhuhr and Asr prayers are consecutive?

The beginning of the 'Asr prayer time, according to the majority of scholars, is when the shadow of everything becomes equal to its length, excluding the shadow at zenith (fay’ al-zawāl). This is the most preponderant opinion. The Dhuhr prayer time ends with the entry of the 'Asr prayer time. The 'Asr prayer time continues until the sun turns yellow; thereafter, it is a time of necessity until sunset. Your previous prayers are valid as long as they were performed after the entry of the prayer time.