The issue with the story of Trojan War is that there can basically be no 'accurate' portrayal of it. The story comes from early 7th century epic(s) which, save for few deliberate archaisms, describe contemporary i.e. 7th century world while telling a story of a distant, heroic past (Bronze age). Anachronistic as the original epic itself might be, movie Troy made a couple of clumsy decisions (in what is otherwise a great, impressive, effort) that left it open to criticism. Those include explicitly setting it in Bronze age in the very opening, for which we don't exactly know what accurate would even be. Also giving heroes like Achilles equipment (helmet most notably) clearly inspired by much later armour instead trying to keep the very smartly designed, vaguely Greek looking, composite look of other costumes (Menelaus' helmet is for example a composite version of so called Kegelhelm from 8th century, but the movie designers made sure the connection is barely noticeable).

That leads us to the questions. It depends what ''that era'' exactly is for us. In the original source materials helmets are pretty much contemporary early bronze Archaic (8-7th c BC) helmets that cover most of the head (Iliad 6.9; 20.397...) are adorned with horseplumes (ll. 3,302;15,514...) and perhaps made from multiple pieces (reminding us of the aforementioned Kegelhelm). In general, metal helmets, or helmets reinforced with considerable amount of metal are known from at least 12-11th centuries BC (Tiryns example). Helmets are certainly unwearable unless padded, even today (metal part is refereed to as shell, helmet is only a complete one with padding). How was that done is not as clear. Some kind of lining certainly existed from early on as the holes for its fastening are clearly visible (sometimes pins used for this purpose very elaborately designed). What was fastened initially (for the first couple of centuries) later became glued to the inside. Few surviving examples of helmet liners come from somewhat later age (6th BC Italy) and include a combination of woven straw and animal hide. That might have been the method contemporary to epics, but not necessarily Bronze age. Although options are, admittedly, limited. Much later source, Aristotle, mentions a particular type of sponge used for this purpose, although he (writing in 4th century) is our earliest source on it. Lastly, helmets from different kingdoms wouldn't differ beyond stylistic preferences of individual workshops which was how these helmets were (unlike what is shown in the Trojan arming scene) acquired.