Follow the methodology of Umm Al Qura Calendar or calculation.

i was born a Muslim, but i have recently started practising, and started to pray on time. To my disbelief i have uncovered that depending on which school of teaching you conform to, the timing of each prayer changes. If for example if I go now to pray Asr prayer, I check the laptop and there are 4 respectable/trustworth sites All Stating Different times? What should i do :(

Prayer | September 12, 2015 2:56 am
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My class duration is such that i miss the salah in jamah but i dont miss the prayer time, only the jamah so can i pray alone in this case after the class and will i be sinful?
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When one is travelling and joins maghrib with isha when does one pray witr does it have to be after the normal ishaa time or before the ishaa time?