How old is Zoroastrianism?

Mary Boyce’s Zoroastrians: Their Beliefs and Practices. She notes in the introduction:
[Zoroaster] was an Iranian, and lived in what for his people were prehistoric times. It is impossible, therefore, to establish fixed dates for his life; but there is evidence to suggest that [his teachings] flourished when the Stone Age was giving way for the Iranians to the Bronze Age, possibly, that is, between about 1400 and 1200 BC.
Zoroaster is thought to have composed not all of the Avesta, but the oldest hymns, the Gathas. The rest of the Avesta is called the “Younger Avesta”, although this is somewhat of a misnomer as certain Yashts are very old as well. The canon of the Avesta is generally thought to have been closed around 600 BC (this is also a traditional dating of Zoroaster’s life by Zoroastrians themselves – I will get to this). The most important piece of evidence is that Zoroaster’s dialect of Avestan is particularly close to the Sanskrit of the Rigveda (to the point of mutual intelligibility). Like the Rigveda, assigned a composition date from about 1700 BC onward, the Gathas give a picture of a stone age society. The name Zoroaster is a Greek folk etymology derived from interpreting his name as meaning “undiluted star”; his Avestan name was Zarathustra (Zartosht in Middle and Modern Persian), usually thought to mean “caretaker of camels” or “loved by camels” (if this sounds like an odd name, compare to the Greek name Philip, which may be interpreted to mean “loved by horses”). However, the world does not develop evenly across all space – Zoroaster’s tribe (conventionally called the “Avestans” after the language) could’ve been particularly poor or isolated, or he could have employed a conservative oral tradition. Per this one may reasonably conjecture that he lived around 1700-1500 BC. Because of the similarities between Gathas and the Rig Veda on several levels (let me know if you want me to elaborate), it is difficult to impossible to know whether the Indo-Aryans took anything from Avestan tradition
One may deduce from the Yashts that Zoroaster must have been from the east of Greater Iran (Greater Iran, or Iranzamin is an area which roughly includes, apart from the modern state, southern Mesopotamia, Afghanistan, western Pakistan, Turkmenistan, Tajikistan and Uzbekistan). For example, Yasht 19:66 mentions Lake Kasaoya “which receives the Haetumant”, corresponding to modern Helmand and Lake Hamun. Videvdad 1 also mentions Sogdia, Margiana, Bactria, Arachosia and Drangiana, all in the Northeast and East of Greater Iran. Though not all of the names are known (and some, like Khwarezmia, are notably absent) we may reasonably conclude that these lands adopted Zoroastrianism relatively early since they have significance in scripture. Unfortunately, our first records of Zoroastrianism (outside the oral tradition of the Avesta, which was only written down in the AD:s) come from Western Iran (e.g. the Behistun Inscription), and the Avesta provides no guidance as to when the faith – or the Iranian peoples – had spread this far.
later Middle Persian tradition assigns Zoroaster’s life time to around 600 BC. This is based on a few lines of reasoning – one, the father of Darius, the third Great King of the Achaemenid Empire, was named Vishtaspa (Hystaspes in Greek). He shares this name with, and was probably named after, the King of Bactria whose acceptance of the eponymous prophet’s teachings is one of the central episodes of Zoroaster’s life. Some have conjectured that they were been the same person, but this lacks any evidence at all and it seems extremely implausible on linguistic and textual grounds (e.g., then why don’t Avestan texts mention Darius and his empire? Why doesn’t Darius celebrate his father’s supposed kingship in Bactria?). Two, there was obviously a desire by the Sasanians to associate Zoroaster with their esteemed ancestors, the Achaemenids, and to maintain that Zoroaster was a figure of greater antiquity, and thus more worthy of veneration, than Alexander (e.g. the Middle Persian Bundahishn mentions Zoroaster living 258 years before Alexander, based on a highly confused generational counting that conflates Cyrus [sic] with Vishtaspa. 258 years is probably derived from 300 – 42 years, where 3 is a recurring number in Zoroastrian tradition, and 42 is the age Zoroaster was when he won over Vishtaspa. Thus him being born 3 centuries before Alexander. This likely reasoning is plain numerology that’s meaningless as far as history goes.)
And when we look at Classical Greek sources, although we cannot take their interpretations at face vaule (for instance they assume that Zoroaster was Persian), Zoroaster is invariably presented as a figure of great antiquity, having lived milennia before the Trojan War. This impression was presumably given to them when they interacted with the Persians. To go off on a slight tangent about the practices of the Acahaemenids, I note that Boyce somewhat uncritically accepts accounts of Cyrus’ personal history, but given that the book is almost 40 years old at this point and this is a somewhat tangential point, that may be excused. More recently, it has been speculated that Cyrus may have been an Elamite (and thus not necessarily a Zoroastrian per se, but possibly a worshipper of Ahura Mazda along with other gods), and that Darius, a Persian and devout Zoroastrian, inserted himself into Cyrus’ family tree – thus, details connecting Cyrus to Zoroastrianism may have been fabricated later. However, she does note interestingly that the Achaemenids did not follow the traditional Zoroastrian practice of burial by exposure, but instead embalmed their kings. Furthermore Herodotus notes that Cyrus’ son Cambyses wished to marry his sister Atossa (interestingly, an Avestan name) and that this was “contrary to custom and law”, which one would think not be the case as cosanguinous marriage (khvaetvadatha) is lauded in later Middle Pesian texts. This cannot be taken at face value, of course, and quoted fragments of Xanthos of Lydia mentions “the Magian men [cohabiting] with their mothers … [and having] like association with daughters and sisters”. Anyway, we cannot really know whether Cyrus practiced Zoroastrianism, but it is quite unambiguous that Darius did.