Help translating two lines of Zhang Shaolin's "Hakka homesickness" (客家乡情) + some weird pronunciations in that song
Hakka speaker from mainland China here. 


there is karaoke lyrics on the video, L2 is 追根由石壁求证 which is correct. Not exactly sure how to translate 求证 here. Maybe: ancestry seeking is proven by the stone walls.
Your own translation is good. "Hakka people in the world are united in remembering homesickness / [And] acknowledging [their] blood is thicker than water." The uncommon order of words is intended for a better rhyme in the song.
团结纪念乡情 (thon ket nyi hiam hiong chin) I hear that's exactly what the singer is pronouncing.
官 is indeed kwon, but still I don't have any problem with the singer's pronunciation.