A capital question.
You were right, Zeibura, in the discussion that prompted this: the Balkans is a big mess of not continuously attested languages and dialects; and the only hints of whether a feature originated in one place rather than another is whether the feature is also present in Koine Greek or Old Church Slavonic—both of which predate the Sprachbund.
We are, as far as I know, out of luck with the future, because neither is the case. The will-future first shows up in Greek about the time all the Balkan stuff shows up, in the 14th century. One of the first instances I know of is in Sylvester Syropoulos’ Memoirs (about the Council of Florence, 1438), when he speaks of Emperor John VIII Palaiologos strongarming Patriarch Joseph II of Constantinople, telling him “you want to agree to Church Union.”
Joseph II wanted no such thing: he was an opponent of Church Union. What John VIII was actually telling him, of course, was: “You will agree to Church Union.”
It is true, as Diana Vesselinova points out, that will-futures are a linguistic commonplace (it also happened in English, after all). But given that every single Balkan language does it, it’s hard to believe there was no influence between the Balkan languages.
You’ve also asked why the will particle is invariable. There’s a parallel phenomenon that was going on in the Balkans at the same time (and this time, we’re pretty sure Greek was the starting point for it): the elimination of the infinitive. We actually see multiple forms competing at the same time in Greek: I will go could be expressed as θelo ipaɣin “I.will to.go”; once you lose the infinitive, you end up with a phrase with both verbs marked for person, θelo na ipaɣo “I.will that I.go”, competing with an alternate phrase with only the main verb marked for person, θeli na ipaɣo “it.wills that I.go”.
The last one is the one that prevailed, with “it.wills that” θeli na ultimately reduced to the particle θa: θeli na > θena > θa. The principle is one of markedness: if the auxiliary only ends up marking futurity, then there’s not much point marking it independently for person. There also would have been analogy with other modals like prepi ‘it.must’ or bori ‘it.can = it is possible’; and θa itself ended up in the same paradigm as the suspiciously similar looking subjunctive marker na.