If timetables differ about the time of Fajr and Maghrib, he should err on the side of caution with regard to his fasting and his prayers
Question

I am currently in XYZ, and because there is no agreed-upon timetable for prayer, I have no choice but to check the prayer timetables issued by more than one organization. I rejected the timetable that goes against the consensus of the other timetables. What I mean by that is that the timetable of one of the organizations shows the time for the Fajr adhaan after 3 a.m., whilst according to many other organizations, the time for the Fajr adhaan is before 3 a.m. Because the issue has to do with fasting, I decided to err on the side of caution and follow the timetable of those organizations who say that the time is earlier. In addition to that, I try to be cautious with regard to the time for Maghrib, and I found that the organization whose timetable I decided not to follow with regard to Fajr shows the time of Maghrib to be a little later than other organizations. Hence, in order to err on the side of caution, I will follow it [with regard to Maghrib], in sha Allah.
My question is: is what I did of adopting a cautious approach valid? More importantly, if I follow the earlier time for the Fajr adhaan, can I pray Fajr at that time, or should I wait until the time given by the other organizations? Please note that if I wait, I will be in a state of doubt and confusion, namely: how can I adopt two times for Fajr, one to start the fast and the other for the prayer? I feel that starting to fast at the earlier time, before the time of Fajr according to the other organizations, is somewhat wrong, meaning that I may reach the conclusion that it is not permissible to start fasting before the time that I have adopted for the prayer begins.
Praise be to Allah.Firstly:
The times of prayer have been clearly explained in the religious texts, and they are connected to observable matters; anyone can work it out with a little thought and reflection.
The time for Fajr begins with the break of the true dawn, in which light extends along the horizon, right and left.
The time for Zuhr begins when the sun passes the zenith, i.e., when it passes the middle of the sky. That may be known by the lengthening of shadows, after the shadows reached their shortest length.
The time for ‘Asr begins when the shadow of a thing is equal to its length, after the sun has passed its zenith.
The time for Maghrib begins when the disc of the sun has completely disappeared.
An-Nawawi said: What this means is that the sun’s disk has dropped completely below the horizon. After it has completely disappeared, it does not matter if some of its rays are still there; rather the time for the prayer begins even if the rays are still present.
End quote from al-Majmoo‘ (3/33).
The time for ‘Isha’ begins when the red afterglow on the horizon disappears.
For more information on the times of prayer, please see the answer to question no. 9940.
Secondly:
Whoever does not know the times of prayer should follow someone who does know that. That includes following timetables.
If the timetables differ, then he should err on the side of caution.
The Maaliki scholar Shaykh Shihaab ad-Deen al-Makki (may Allah have mercy on him) said in Irshaad as-Saalik (1/13): If someone is uncertain as to whether the time for prayer has begun, he should not pray; rather he should delay it until he is certain or thinks it most likely that the time has begun. End quote.
You should err on the side of caution with regard to the fast by starting to fast at the earlier time given [in the timetables], and you should err on the side of caution with regard to Fajr prayer by praying at the later time. Thus you will be certain that your fast and your prayer are valid.
In order to err on the side of caution with regard to Maghrib, you should break your fast and pray at the later time given.
You could go out to an area of flat land and see the sun set and its disk disappear completely, in order to verify the timetables that you have, because working out the time of Maghrib is easy, unlike Fajr.
There is nothing wrong with using two times for Fajr, one for starting the fast and the other for praying, so as to be on the safe side with regard to two acts of worship, for one who is not sure whether the time given is correct.
And Allah knows best.