There was also a major disparity in terms of equipment and training between the professional core and the rest of the army.

This doesn't seem to have been true among the Gauls, although it does seem to be so when Caesar speaks of the Germans and it's certainly true with his description of the Britons. A lot of supposedly Gallic customs are not Gallic at all, they are British, which includes descriptions of armorless warriors with little in the way of shields or helmets. From what we can tell Gallic armies tended to be highly developed in terms of their equipment--leather shields are not particularly hard to make, and from what we can tell helmets at least were relatively common among Gallic states. The Gauls were, after all, incredible metal-workers, and we have lots and lots of evidence for widespread metal armor. Of course, archaeology can only get us so far, especially when most finds are at grave sites. But it's telling that Caesar does not describe any of the Gauls the way he describes the Germans and Britons in terms of dress. Caesar says that the Britons often fight naked, or stripped above the waist, and though he does not say if the Germans do the same he claims that they leave much of their bodies bare, covered mostly by loosely-fitting cloaks. The Gauls are always described as clothed, and in battle there's no indication of any Gauls being unarmored or without a proper shield, which features prominently in his discussions of the Britons. Speaking of shields, I don't think we've ever come across a depiction of a Gaul using a small shield or have ever unearthed one--they're uniformly these rather big oval leather shields. No doubt the rank-and-file was not as well equipped as what Caesar calls the "knights," but there's no indication to suggest that they went into battle unarmored or with especially poor equipment. The enormous wealth of material finds of metalworking suggests that this makes a great deal of sense--Gauls made lots and lots of armor.

Also about the troop numbers: I understand how urbanized societies like Roman and the Greek city-states could effectively call up large armies but I'm not sure if the much less centralized, less urbanized Gauls could do the same.

The Gauls appear to have been fairly urbanized, so far as what are essentially still tribal societies go. Their cities were relatively large, and well-developed enough for Caesar to call them oppida. Caesar's estimation of 80,000 men garrisoning Alesia is probably pretty accurate--they came from a number of nearby states. The city was large enough to keep them housed, supplied, and fed for the duration of the siege--no small feat. Gaul is an extremely fertile place, and archaeologically there's every indication that Caesar is perfectly right in separating the lack of German agriculture from the Gauls. Nor was Gaul quite so divided as all that. The lands which each tribe might contain were usually rather a lot larger than those of a Greek city, and they were a great deal more fertile. The Gauls practiced agriculture at a level that could sustain fairly large populations, so it's not too surprising that they might be able to field much larger armies than Athens or any single Greek state--Greek states like Athens, after all, only called up citizens (or sometimes metics), a custom by which Gauls would not be bound.