Were the philosophers of Ancient Greece aware of Eastern Philosophies, such as Zoroastrianism or Buddhism? Is there any mention of them, either directly, or similar concepts in existing writings?
The Ancient Greeks were definitely aware of Zoroastrianism-(in fact, the name, "Zoroaster", is a Greek translation of the original Farsi name, "Zarathustra").
The main reason why the Greeks were aware of Zoroastrianism-(and greater Persian culture), is because the Persian Empire conquered Greco-Anatolia-(present-day Turkish coast) 2500 years ago and also attempted to conquer mainland Greece shortly thereafter, (but failed in doing so).
The political and economic landscape of the greater Aegean region 2500 years ago, consisted of a large Hellenic population culturally intermixing with a smaller, but very powerful, Persian colonial population. One of the best examples of Persian Zoroastrian cultural influence on Greek Philosophy, was Heraclitus of Ephesus-(circa 500 BC/BCE).
Heraclitus lived under Persian colonial rule in the city of Ephesus all his life. During his time, Heraclitus penned many famous aphorisms and sayings, such as, "War is the Father of all things", as well as, "A road going up and down is one and the same". His sagacious proverbs were perhaps the earliest examples of Dialectical Philosophy, which, judging from the time period and geography, may have had some Persian theological influences. Zoroastrian Theology is primarily based on a Warring with opposites, a type of metaphysical duality that seems to be never ending.
In addition to its theological dualism, Zoroastrianism-(and Zoroaster himself), believed that Fire, as Light, was the most noble and beautifully virtuous symbol reflecting the might and wisdom of God. Interestingly, Heraclitus appeared to have borrowed some of these ideas from The Persian Zoroastrians. Heraclitus did place an emphasis on Fire, as the First, the Greatest and most foreboding of all the Elements.
So when examining Heraclitus' sayings, including his emphasis on Fire as the Greatest of all the elements, it would not be surprising to learn that he was likely influenced and literally surrounded by, Zoroastrian Clerics, as well everyday Persian Zoroastrians, who he probably interacted with in the marketplace, as well as elsewhere in the Cosmopolitan City of Ephesus.
But, it is also important to note that while Heraclitus was probably influenced by Zoroastrianism, his sayings and even his emphasis on the elemental presence of Fire, were still independent, novel philosophical ideas and NOT a mere recirculation of religiously based ideas.
I don't remember any references but Zoroastrianism was known.
"The religion named after him is not attested to historically until the 5th century BCE, where it appears in Greek sources."
Zoroaster's name in his native language, Avestan, was probably Zaraϑuštra. His English name, "Zoroaster", derives from a later (5th century BCE) Greek transcription, Zōroastrēs (Ζωροάστρης), as used in Xanthus's Lydiaca (Fragment 32) and in Plato's First Alcibiades (122a1). This form appears subsequently in the Latin Zōroastrēs and, in later Greek orthographies, as Zōroastris.
Although, at the core, the Greeks (in the Hellenistic sense of the term) understood Zoroaster to be the "prophet and founder of the religion of the Iranian peoples" (e.g. Plutarch Isis and Osiris 46-7, Diogenes Laertius 1.6–9 and Agathias 2.23-5),
Zoroastrianism enters recorded history in the mid-5th century BCE. Herodotus' The Histories (completed c. 440 BCE) includes a description of Greater Iranian society with what may be recognizably Zoroastrian features, including exposure of the dead.
And in this article about the "Hellenistic" period (~300 BC) there are some info about Greek interactions in far east
Several philosophers, such as Pyrrho, Anaxarchus and Onesicritus, are said to have been selected by Alexander to accompany him in his eastern campaigns. During the 18 months they were in India, they were able to interact with Indian ascetics, generally described as Gymnosophists ("naked philosophers"). Pyrrho (360-270 BC) returned to Greece and became the first Skeptic and the founder of the school named Pyrrhonism. The Greek biographer Diogenes Laërtius explained that Pyrrho's equanimity and detachment from the world were acquired in India. Few of his sayings are directly known, but they are clearly reminiscent of śramanic, possibly Buddhist, thought: "Nothing really exists, but human life is governed by convention. ... Nothing is in itself more this than that"
Another of these philosophers, Onesicritus, a Cynic, is said by Strabo to have learnt in India the following precepts: "That nothing that happens to a man is bad or good, opinions being merely dreams. ... That the best philosophy [is] that which liberates the mind from [both] pleasure and grief".