The first problem there is that ,due to the popularity of "Celtic" romanticism and Celtic Revival, a lot of features are popularly attributed to all of Celtic peoples without necessarily being attested or verified in sources, either historical or archaeological Druidism isn't an exception to this rule.

Even if, thanks to exploiting ancient and medieval sources as well archaeological data, we might have a relatively clearer perception of Druids, it still a fragmented image where various interpretation create important academic debates.

In Antiquity, Druidism is only mentioned by Greek or Roman authors as a Gaulish and British feature : never the word or an equivalent position is described for Celtiberians, Danubian Celts or Irish; it doesn't negate the possibility of their presence in these peoples, but the argument tends to revolve about the axiom of Druidism being pan-Celtic, which is largely unproven.These sources first identify druids in the late IIIrd century BCE but it's possible that they were known by Greek scholars as far as the Vth century, after centuries of contact with Mediterranean Celts in comparison with Pythagoricians. Did druids only appeared with the LaTenian period, however? This is the other bone of contention between historians arguing in favour of an earlier, proto-Celtic institution, and those arguing in favour of a Gaulish institution born out of the contact with Mediterranean peoples (trough trade or mercenariate) and the transformation of local polities in the VIth to Vth centuries BCE^(1).For the sake of transparency, I must say I rather agree with the latter and follows essentially this perspective in this post : even there, the existence of "pre-Druids" existing from the late Bronze Age, is still considered possible.

These Gaulish and British druids had an important set of responsibilities, ranging from organising religion to being philosopher, as well as scholars and judges.However we can still see a functional slip of Druids, still considered as seers in the Vth century, when Uates took over this role in the IInd; which possibly hints at the role of the aforementioned "pre-Druids", or even as sorcerers of sorts which would be essentially cast away later in Gaulish Druidism in favour of a more rationalist figure closer to a Greek philosopher or a theologian than a priest (bards and uates being unfortunately ignored by Caesar, hence a later mix up of Druids as seers, sacrificer and priests).In this perspective, contacts with Greeks since the VIth century, the Rhone trade road entering deep in Gaulish and Celtic heartlands, might have well played a role there, especially given the trope of Gaulish philhellenism (hellenic influence being obvious in regions closer to Massalia, as it appears in the oppidae of Ensérune or Entremont; but also further as demonstrated by the Vix Krater) new ideas colliding with old ones in the early Celtic states of the region, filling a social vacuum with the decline of Halstattian aristocracies in the VIth - Vth centuries; partly explaining the cultural rupture between Halstattian and Latenian cultures.Ancient Greek made comparisons with Druids and Pythagoricians, and the fortune of the latter in Greek Italy might provide something to the idea early Druidism could have been partly and indirectly inspired by Pythagore's disciples but as well by Orphic tendencies among Greeks, especially with the stress on metempsychosis. (Peoples closer to Mediterranean Sea are also the same that seem the less marked, if at all, by a Druidic influence; which would stress the indirect transmission and an original emergence of Druidism among Gauls).

Gaulish sanctuaries might be an interesting feature too on this regard : the appear, almost out of the left field, in the IVth and IIIrd centuries without known predecessors. While superficially Greek-like on the exterior, the interior is open-aired and both the sacred wood (nemeton) and the altar are close to each other.It would be tempting (and it is done, truth to be told) to associate this brand new religious materiality to Druidism : chronological correspondence isn't really perfect tough, and it would require new archaeological discoveries to be more decisive when it come to Britain (Britto-Roman temples, as Roman temples in Gaul, being quite distinct from the aforementioned sanctuaries)On the other hand, it was previously thought to be rather a northern Gaulish thing but equivalent had been found in southern Gaul too, namely in Le Caylar.It's hard not to hypothesize a Druidic presence in Germania, where people share essentially the same culture than Gauls until the Ist century BCE, but there's a lack of historical and archaeological sources to propose something strong enough; although speculating about their presence there isn't really implausible; that the known Druidic annual council took place in Gaul (in the territory of Carnutes, believed to live in the center of Gaul) and the comparison with "lay" Gaulish council might indicate that neither British druids or their hypothesized Germanic colleagues took part in these.

Druidic presence in Britain is nevertheless attested for the Antiquity trough Roman sources, which giving the important ties between Gaulish and British peoples is quite logical, as well as an increased presence pointed by Caesar since the IInd century (probably because Roman influence was detrimental to Druidic teaching even before the conquest). Welsh sources are too scarce to be really definitive, but could hint at a pre-Roman reality.Presence of druids in ancient Ireland, however, is a challenge : there's simply no mention of them for the period and only medieval texts which depict them as different figures than British or Gaulish counterparts : wizards, enchanters, brewers, sorcerers, or even quacks. Giving the relative isolation of Ireland, it might be possible that an equivalent of "pre-Druids" remained there as an archaic feature, possibly called druids by later chroniclers linking them to what they knew of Gaulish or British pagan religious figures.

Eventually, what we call Druidism from ancient sources about Gauls and Britons might have been only one of the religious (understood as an institutions) traditions of the various Celtic cultures, which could be compared only to what might have existed in Ireland as an isolated archaic survival; but not efficiently to Celtiberians or Danubian peoples due to the utter lack of historical and archaeological evidence.

Regarding your second question : aforementioned contacts between Celts and Greeks don't seem to have taken place in Balkans, mostly because migrations to Middle Danube and Balkans took place only in the IIIrd century BCE; but also because contacts there took a more confrontational look with raiding expeditions. While druidic presence is possibly hinted at trough the Drunemeton of the Galatians, it might be due to a Gaulish influence rather than a local "re-creation" of Druidism (although Druids themselves aren't accounted for in Galatia, maybe due to an early and intense Hellenistic influence).It is only at this point that Celtic influence (either due to migration of Celtic or Celticized peoples; or Celticization trough trade or relations of local peoples) can really be pointed at in Transylvania, when Druidism is already attested in Gaul.

The (broken) source in the Wikipedia article seems to comes from Carl Wadman and Catherine Mason's Encyclopedia of the European People; where a lot of assumptions made about Druids (as being pre-Celtic, unmistakably seers, not taking part in fights, direct continuity between ancient and medieval Druids etc.) could benefit from actual sources, and some other are blatantly wrong (Caesar never mentioned Anglesey as a Druidic centre, neither Bibracte by the way). Both of the authors seems to be freelance writers of pop-history and, while I don't want to seem lacking respect to them as persons, you'd be better off with actual historians of Celtic peoples (Druids : a very short introduction, by Barry Cunliffe for instance even if you'll find he describes a much different perspective that the one in this post)

Whoever put this source in the Wikipedia article, furthermore, doesn't seem to have even actually read it, as the author states that "The Dacian priestly class may have emulated the Druids of the Celts" (it's technically possible, but a direct Pythagorician or Orphic influence from Greeks is as if not more plausible) which you could recognize as the exact contrary of the Dacian priestly class may have influenced the druids of the Celts

- The Celtic Gauls: Gods, Rites and Sanctuaries; Jean-Louis Brunaux; 1988

- Les Druides - Des philosophes chez les Barbares; Jean-Louis Brunaux; 2006

- The Druids; Stuart Piggot; 1968

(on a more Indo-Europeanist and Pan-Celticist take)

- Les Druides; François Leroux, Christian Guyonvarc'h; 1985

There are many similarities between the Brahmin class and druid class which point towards a more culturally ancient source for this group of people than you describe. In this interpretation of the data, the druidic tradition would have been transmitted first through greece and then through the hungarian plain to areas north and west of europe. So the people of gaul would have been 'celtisized' by the people of transylvania. The culture originated southwest of the Ural mountains. From what I understand this culture moved east to west? Or did the indo-european culture originate in northwest europe?