this is the big one; the reason shaman/priests were at the top of the hierarchy in all post-agrarian cultures is because knowing when to plant seeds was the most crucial societal role in changing from hunter-gatherer to domestic agricultural, fueling population density and allowing even more specialized roles.
Persian astologer-priests were literally the magi from which the word magic is derived, so yes.
True. [Well, they were actually Medes, Iranian astrologer-priests is more accurate.]
https://iranicaonline.org/articles/Magi
The Magi were one of the tribes of Medes and the designated priestly tribe (think Levi). And likely from exposure of Medes (possibly Kurds of today) to Mesopotamian cultural centers, specially Babylon, the Iranian tribes got into astrology and astronomy. The Iranians started out as nomadic herding tribes (Abel) before settling (Cain) and adopting urbanism in what is now called The Iranian Plateau.
So we Iranians (Medes or Persians) did not invent astrology - we almost certainly got that from Babylon and to this day our calendar is the Zodiac, of four season with 3 months each, commencing on Spring Equinox. For example Khordad (3rd month of spring) is Gemini.
https://en.wikipedia.org/wiki/Zodiac
"Around the end of the 5th century BC, Babylonian astronomers divided the ecliptic into 12 equal "signs", by analogy to 12 schematic months of 30 days each."
This, imo, is where the 12 sons of Jacob (tribes of Israel) and the 12 Imams of Shia come from. All this numerology fascination is Babylonian in origin (though possibly they themselves got it from Egypt).
Same with the floats. How else would you carry statues around?
In general terms, if you look long enough into enough cultures, you start seeing patterns everywhere. But that doesn't necessarily mean that connections exist, or that they are more than superficial. Good example would be various pan-nationalist projects of the 20th century.
But not where they end.
Using a Jungian (or gnostic/mystic) analytical framework, Isis and Mary represent the 'pure ground of emergence', and their son, 'the redeemer/the chosen'. This then is an inherent 'constellation' of human 'collective unconscious' that cyclically re-emerges as epochs change, taking on the garb reflecting the new cultural matrix.
The mystic/spiritual idea expressed is this: by purifying one's mind (Mary the chaste) there emerges a new center of conscious mind (the Son) who is 'guided and chosen' by God (i.e the Universal Mind). This 'son' is "persecuted" and "killed" but resurrects (Jesus and Osiris).
The sum of all judgement calls in this case is however tainted by vehement opposition to the notion from devout Catholics (or even culturally loyal Catholics), who naturally can not bear to think that the Virgin Mary is connected to heathen gods whatsoever. So there is that.
From my point of view it is only natural that iconography and traditions are transferred from one religion to another as the different geographic regions historically have moved from one religion to another. Many times such transferal has even been a conscious tactic as a way of increasing the acceptance for the new beliefs.
Many (most?) cultures that are not connected to the Mediterranean traditions don't carry statues of gods around at all.
So that covers two other major civilization centers on this planet. What does that leave us with? Maybe some cultures in sub-saharan africa? But there's definitely some connection there. So Americas?
TLDR: Opposite is true, carrying symbols of your religion, either by hand or in a vehicle, is extremely widespread.
https://en.wikipedia.org/wiki/Temple_car https://en.wikipedia.org/wiki/Dragon_dance