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Phillip's effigy was already being carried in the sacred procession with the Olympian Gods before his assassination. A few Greek personages had already been accorded divine status even before Alexander. Even Romulus was deified as the God Quirinus. I think Alexander was influenced by the Oracle at Ammon-Zeus in Libya of his divinity than by any Persians.

The Persian Monarchs were never worshipped as divine by the priests of Ahura-Mazda as they were strict monotheists. Alexander borrowed the Court protocol of the Persians which was probably borrowed from Mesopotamians. As for the term "Augustus" being derived from Persian, I think that is a stretch. Both Latin and Persian are Indo-European and share certain root words. It is more probable that they developed independently from a common source.

The Persian Monarchs were never worshipped as divine by the priests of Ahura-Mazda as they were strict monotheists.

Not quite correct. While they were not supremely divine as Ahura Mazda, and subordinate to him, they were spiritually clearly of (quasi)divine status. Shapur's inscription reads:

"Worshipper of Ahuramazda, the god Shapur, king of kings of the Aryans and non-Aryans, of divine descent, son of the Mazda worshiper, the god Ardashir (Artaxerxes), king of kings of the Aryans, grandson of the god-king Papak."

The king and his royal predecessors are subordinate to Ahura Mazda, but clearly divine.

The inscriptions for Shapur II and III say "from the divine race of God", although in this case it's debatable whether this could mean all Iranians, and not only the King.

Whether they were actually worshipped is another thing, but they saw themselves as godlike.

I didn't say that Augustus is Persian in origin, but Avestan, which is, as you correctly say, the common root. The "aojishta" was to the Zoroastrians the attribute of the Fravashi, the angel-spirits of great personalities (including the King). Maybe I should have contexted that point a bit more.

I think Alexander was influenced by the Oracle at Ammon-Zeus in Libya of his divinity than by any Persians.

This may be correct, the Egyptians (and the Greek oracle in Siwa obviously saw themselves as having authority to declare Alexander Pharaoh) gave their Pharaohs also divine status, however historical record shows clearly that Alexander tried to establish himself as legitimate heir of the Persian kings, adopting their role, marrying a princess, and taking over their traditions, dress etc. much to the chagrin of his Greek/Macedonian comrades... and this persianate hellenistic traditions were later emulated by the Romans. I.e. the "proskynesis" was again adopted by Diocletian.