Is a Muslim's prayer before its time for Fajr and Maghrib, and their fasting, in countries that change their clocks between summer and winter (losing an hour in winter), valid given the significant difference in prayer times that occurs in a single day, and what is the precise analysis of this issue?

The issue of daylight saving time and standard time is a matter of conventional organizational arrangements. It does not alter the reality of the prescribed times for prayers and fasting. Rather, it is a change to the local time. For example, if the time for Fajr prayer shifts from 5:26 to 4:27, it means that the Fajr time has only increased by one minute compared to the previous day, and that people will set back the clock by a full hour. Daylight saving time is moving the clock forward by one hour, which delays the onset of darkness and provides an hour of daylight for recreation.