Is the story about the movie 300 with King Leonidas and his Spartan Troops holding off King Xerxes massive Persian Army blown way out of proportions or is their more truth to it?

You already saw the link to my podcast episode and the posts with further detail in that thread, so I'll just focus on your specific questions.

How long did they hold the mountain pass?

According to all sources, they were at the pass for about a week, of which the last 3 days were spent fighting. Leonidas fell in the course of the third day, and by evening the pass had been cleared.

What type of people did King Leonidas Recruit?

Leonidas' army consisted of a fraction of the militias of all Sparta's subject allies, plus some militia troops from the regions close to the pass at Thermopylai. If we compare the size of the contingents at Thermopylai with those that the same states sent to the battle of Plataia next year, it seems Leonidas called for about 1/10th of the levy of each ally. It was up to each state to select the unlucky ones who were to follow Sparta's command. In cases where only a part of the levy was called, the lot usually fell on the younger men (aged 20-39), often from the wealthier strata of society.

As for his own troops, there is a tradition that says he selected only men who already had sons, so that their households would not be extinguished if they fell, but we don't know if this is really true. Either way, the 1,000 Spartans were probably deliberately selected. One thing we know is that the 300 Spartiates among them were not the royal guard of 300 hippeis, since Herodotos only mentions that unit later on.

Why did the Exile choose to help the Persians?

The story of 300 merges two people here. The exile in Persian service at Thermopylai was the deposed Spartan king Demaratos, who had chosen to live at the Persian court years ago because of the lifestyle and influence it afforded him. This was a common choice for prominent Greeks who had fallen from grace. Meanwhile, the Greek who told the Persians about the pass (at least according to the story) was a local man from Trachis, who probably hoped to be rewarded.

What happened after the revolt?

I'm sorry, I'm not sure what you mean here. What revolt are you referring to?

Who even wrote down this epic event to keep memory of it?

The earliest version of the story was spread by the Spartans, recorded long after, and now only preserved in much later sources. The main version that we know (which is quite different from the earlier one) was written down by the historian Herodotos of Halikarnassos in the 430s BC (50 years after the battle).

Were there other big Greek nations at the time and just nobody knew about them cause history only records the winners?

There were, and history most definitely records them. Throughout Greek history, Sparta's main rival was actually the state of Argos, in the northeastern corner of the Peloponnese. The Argives were neutral in the war against Persia, partly because the Spartans refused to let them lead the Greek alliance, and partly because a recent defeat against Sparta had decimated their population of fighting-age men. The other big and wealthy state of the Peloponnese was Corinth (south of Megara, which appears in the game). Further afield, probably the greatest Greek power at the time was Syracuse on Sicily. This state also didn't participate in the Persian Wars because Sparta would not give up the leadership, but this proved fateful in the case of Syracuse, since it allowed them to defeat a Carthaginian invasion around the same time. There are countless other states that could be mentioned (we know of approximately 1000 Greek states in the Archaic and Classical periods), but these are the most prominent ones at the time.