Does the sentence lose any of its meaning without "belum".
Yes, it will have the opposite meaning.
"belum pernah" = "never".
"pernah" = "ever".
Does using "terjadi" instead of "menjadi" imply the past tense?
No, it doesn't imply the past tense.
"menjadi" (active transitive verb) = to become.
"terjadi" (passive intransitive verb)= happened.
This is the "accidental" type of ter-verbs, meaning that the action of the verb occurs in an unintended/uncontrolled/unexpected/accidental way.
Ah, I see, so it's "menjadi" when there is an object, but "terjadi" when there isn't! OK, so what about "belum pernah" and "tidak pernah". What's the difference? Is it that "belum pernah" implies you intend to do thing tersebut yang you never did, but "tidak pernah" includes no such undertone? 0.o
Is it that "belum pernah" implies you intend to do thing tersebut yang you never did, but "tidak pernah" includes no such undertone?
Yes, that is more or less the difference.
"belum" = not yet.
"tidak" = not.
"tidak pernah" is simply saying that you have never done it before.
"belum pernah" is also saying that you have never done it before, but it could also imply that you have the intention to try it.