At the time of the battle of Thermopylae, the helmets may have had crests running front to back. It is also possible that some helmets had raised crests (still running front to back). Historically, the kings and commanders wore their crests side to side, and at the battle that followed Thermopylae (Plataea), commanders were wearing side to side crests. I think some artistic license was taken to make Leonidas stand out (more than he would have with a side to side crest in a force all wearing front to back crests). At that time, it is probably likely that shields were individualized, but the matching lambdas were impressive. In fact, the matching shields probably happened pretty soon after Thermopylae. At around the same time, the Spartans discarded their bronze curiasses, but yes, at Thermopylae they were probably wearing those along with bronze greaves. We are just lucky (unluck?) that they were wearing pants or underwear or whatever those things were. Some Greek soldiers fare depicted fighting naked at the waist.

The Spartans were leading a larger force until the path behind them was discovered by the Persians. At that time they dismissed the bulk of the force. All that remained were the 300, 400 Thebans and about 700 Thespians under Demophilus.

Killed in the first phase of fighting was Leonidas himself, but that wouldn't have made a compelling movie (Xerxes lost two brothers in the same timeframe).

Surprisingly (or not), the line about fighting in the shade is historical (fact or fiction).

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