Day and night

This letter is important to clarify our way of the timing a "day" and "night" according to Islamic and Christian calendars. Day begins by the sunset time, in our Islamic calendar, on the other hand at midnight (I will call it night), according to Christian calendar.
Therefore date changes at the evening in Islamic world. But our system in Pakistan goes the other way. Take example of 26th of Rajab, the Shab-e-Mairaj was celebrated on the 27th of that month which was not correct in my opinion and (Islamic as well), so we did that in wrong way.
The date of Shab-e-Baraat is 14th of Shaban. I insist that Shab-e-Baraat this month should be celebrated when the sun of the 13th Shaban is set, that moment night begins and the Holy night (night between Saturday and Sunday). I spent years in Middle East. Once I was in Bahrain in the month of Muharram, the cinemas were closed. On the 10th of Muharram my friend came to me and asked let's go to cinema. I said today is the 10th - the holiest day of all. He said that at the sunset of 9th, date changes and we are now in 11th of Muharram.
Another example of Ramazan moon that is sighted on the last day of Shaban and we go for Traveeh prayer same day. But we fast next day. How you prove it correct that Traveeh in Shaban and Roza in Ramazan? I ask my religious scholars, or Khateeb-e-Masjid to correct the system and me on the whole.