بسم الله الرحمان الرحيم 

البدر   it's the moon in its full state of lightness and the Arabs make this position an example of beauty so when they wanna say to someone he/she is beautiful they compare it with البدر and say he/she is like البدر but most often with men because البدر is a male noun in the Arabic and here in this example it's refer to the prophet (صلى الله عليه وسلم ) and the phrase (طلع البدر علينا ) it's like when you say (we have the sun rises or the sun is rises upon us ) and ( من ثنيات الوداع ) it's mean ( from ثنيات الوداع :D) because ( ثنيات الوداع ) it's noun of mountains in EL MADINA so now the first phrase it's mean the prophet صلى الله عليه وسلمwhich he is البدر rises upon us from ثنيات الوداع and the last phrase here (from  ثنيات الوداع ) it's doesn't mean his origin or from where he came from it's described and inform us the place which the prophet صلى الله عليه وسلم enter to EL MADINA when he made his migrate from MAKKAH ......so here this poem they said the people of El MADINA they made it when they knew that the prophet صلى الله عليه وسلم is coming over them ......but the truth is that is not correct because the prophet صلى الله عليه وسلم he didn't enter from "ثنيات الوداع " and who wants more details about that should be read his book ZADO EL MA3AD (زاد المعاد ) and among his speech about this he said  ( ,,,and it's so clear that story is wrong because ثنيات الوداع you can't see it if you come from MAKKAH it's appear just if you come from EL SHAM ....)

the moon rises upon us,, from among Thaniat Elwadaa
we ought to thank allah ,, as long as people call Allah
O our messenger ,, You come according to the obeyed order 
You come and honoured Almadinah ,, welcome O best apostle 
the clear light rises ,, the light of the finest messenger 
a light of safe and peace ,, a light of truth and certaunity 
Allah sends Him ,, as a merciful to the whole world 



this is my humble trial ,thanks in advance 
 

subhanallah, I wish I could help, thanks fordiscussion, jazakmullaha khairan