Is it obligatory to make up the fast if one broke it based on Qatar Channel's call to prayer, which precedes the adjacent mosque's call to prayer by 40 seconds, and is the fast considered valid in this case?

It is permissible to act upon the information provided by a trustworthy source regarding the entry of prayer time. Indeed, a reliable muezzin who is knowledgeable of the timings may be relied upon for the entry of time by both those with sight and the blind, whether the sky is clear or cloudy, because he typically does not call the adhan except at the correct time. Therefore, there is no harm in breaking the fast upon the adhan from the aforementioned channel. If the two muezzins or two calendars differ, then you should follow the more reliable of them. And as long as the difference is slight, being cautious is better.