If i sync my iphone would jailbreak be removed

so i have my iphone 3g. model A1241, iOS version 4.2 .  its american, att. my cousin sent it to me from houston texas. i currently live in monterrey mexico. so my i took it to get a jailbreak for it to work here in mexico with the phone company TELCEL. so my doubt is that i want to download the app Voxer, and when i go ahead and download it, it says i need the version iOS 4.3  . but my other friend has an iphone exacly like me, but on his iphone it did allow him to download Voxer, how can i get mine fixed? i took it to the guy who fixed it, and i told him to put the new iOS version on my iphone, he said is not possible, if he does the new version that would delete the jailbreak. so i suggested to put the iOS 4.3 and then do the jailbreak but he said the jailbreak will be useless with the new iOS 4.3 . basically i wont be able to use my iphone to make calls and texts, it would just be a ¨show¨ phone. how can i fix it? what can i do?  so also my other question, is about itunes, how can i add music and videos, etc to my iphone through itunes? do i have to sync it, if i sync it would it delete all my apps, and the jailbreak?? is there another way to add music besides the itunes, cant i just simply drag the music file to the ipod in my iphone?? how can i NAME my iphone? HELP! i sorta new to the iphone, always have loved it, its so convenient and so user friendly. its like a perfect personal assitant. but i just dont know what do to, actually im scared to change stuff on my iphone since supposely, whatever i do i can risk erasing the jailbreak, maing my iphone useles... i really appreciate ur feedback my friends. sincerly ME, from MEXICO, Monterrey