Is the fast valid if the fasting person drank after hearing a distant adhan that was not relied upon, then stopped drinking upon hearing the adhan of the nearby, relied-upon mosque, with food coloring remaining on the tongue after dawn, knowing that the muezzin relies on timings or the Adhan of Mecca and suffers from scrupulosity?

If you abstain from things that break the fast upon hearing the Fajrathan, then your fast is valid, and the sound you heard previously does not harm it. If you drank water one or two minutes after the adhan, your fast is valid and you do not owe a make-up fast, because the adhan currently relies on the timetable due to the difficulty of seeing the dawn, and the calendar usually anticipates it as a precaution. As for eating food that changes the color of your tongue, it does not invalidate the fast. The best cure for obsessive thoughts is to ignore them.