To expand on the second question in the topic: I've read before we can verify if written accounts are accurate by comparing them to other writings from the same time and looking for minor details and incidental events that match up. (As an example, I've read this is how we know parts of books in the New Testament describe actual events and how we know some of it is not at all true.)
Herodotus is the only reliable source that far back. How do can we know he writes the truth with nothing to compare or verify it against?
I checked the FAQ and did a search and, to my surprise, could not find anyone else asking this. My apologies if I missed a post. It seems like something that would have been asked by now.
The short answer is that it's difficult to differentiate. Most ancient historians, Herodotus included, are known to have embellished events in their writing, and they likely did so for a number of possible reasons: ethnic or political biases, a desire to draw attention through dramatic or exotic stories, or a desire for personal popularity, among others. Separating fact from fiction is made much easier if there is accompanying archaeological evidence, other works from contemporary authors, or economic records (including army payrolls, tax ledgers, trade records, etc). Without these, corroborating the truth and accuracy of stories and accounts becomes very difficult.
Perhaps the main reason why Herodotus is seen as being so reliable is because of the general approach he took to the study of history, which stressed an investigative method that sought to establish a narrative based on systematic and critical analysis of numerous sources. Despite this, Herodotus still embellished his work and was even called out for it by other historians living after his time (Cicero said of Herodotus's work that it is full of "innumerable fabulous tales"; On the Laws I, 5).
But on the whole, because Herodotus sought to study and convey history through a (relatively) objective lens, and some of his accounts have been borne out by other analyses and evidence in both past and present, historians today generally consider him reliable. While the veracity of minute details may be questionable, he does provide a fairly accurate framework of Greek history, broadly speaking. Hope this helps!
It is worth noting that Herodotus is not the earliest reliable historian, nor is he the only reliable source going that far back. Written sources describng historical events go back very far indeed, particularly from Egypt and Mesopotamia. Some of these can be quite detailed, such as the funerary inscriptions of Ahmose, Son of Ebana, an Egyptian military officer during the sixteenth century BCE. And many of these are quite reliable, such as the scrupulous recorders of the Babylonian temple archive.
Why Herodotus is the first historian is because of what a historian is: an author (what you might define as "someone with a meta-textual presence") who gathers and compiles information into a narrative. The minutes of the US Congress, for example, is a spectacularly detailed and reliable account of historical events, but it isn't a history because it is only a bare recounting of facts. There is no historians, therefore there is no history.
Earlier accounts tended to be highly autobiographical in the form of royal chronicles (I, King Adur-Badur-Dadur, great king, smote Ur, which had risen against the god) or is the maddeningly terse temple archives which were essentially references of religiously significant events (In the year five, the god was taken out of the temple in procession. The king of Assyria sacked the city, utterly destroying it. In September, a calf with two heads was born). Compare that to Herodotus, who will walk you through various events, highlight connections, digress to emphasize the significance of what is being described, and so on and so forth. It isn't that Herodotus is more reliable than previous accounts, it is that he is n a different genre.
Common sense can be helpful in some cases. For instance, when Herodotus tells us that there were 2.5 million men in Xerxes' army at Thermopylae I don't think many would leap to defend Herodotus figure. Provisioning that amount of men with the agricultural and organisational capabilities would be an insurmountable challenge. We can therefore put paid to some of the things he tells us and come up with more 'reasonable' conjectures and estimates.
It is also possible to confirm certain parts of his story from other sources. For instance, if he tells us that someone dedicated a temple, placed some treasure to a temple, raised a monument in honour of a victory and so on it is sometimes possible to track these physical objects and therefore get some corroboration for the events associated with them. If I remember correctly the treasure that Croesus donated to the Oracle at Delphi is attested in Pausanias. So the fact of the treasure's existence is not in doubt, but we have to trust Herodotus on the string of events that led up to the donation.
As for the speeches, everyone has their own spin on if they are the actual words spoken by Thucydides, Xerxes, Darius and so on. My personal view is that they are either the words that were spoken, Herodotus claims to have done some source gathering work and may have managed to find accurate accounts, or the speeches are intended to preserve the impression of what was said if not the words themselves.
The fact remains however that Herodotus is a very tricky source and since we have to use him in isolation, differentiating fact from embellishment and pure fantasy is difficult and often impossible.