Ah, a question about Zoroastrianism! Always fun to see. The broad approach of my answer will mainly rely on the perspective offered in Mary Boyce's Zoroastrians: Their Beliefs and Practices (especially the first three chapters).

There's one thing that needs to be understood when discussing what is variously called "Iranian Paganism" (the term Boyce uses), "Old Iranian Religion" (The term I will use), or (problematically) "Iranian Polytheism", and that is that our understanding of what it was relies entirely on Avestan material in the Zoroastrian scriptural canon, as well as comparative analysis with the Rigveda, plus Central Asian archaeology. Now, I will address your questions point by point, starting with the last ones.

And how widespread was the pre-Zoroastrian belief system?

Hard to say exactly, but if we go back to the Indo-Iranian era (say, 2000 BC and further back), then probably much of the Central Asian steppe, i.e. southern Russia, Transoxania, etc.

Did it persist in Iranian-speaking peripheral areas like Tajikistan and Afghanistan?

These areas are not as peripheral as you might imagine, quite the opposite, they are close to or part of Bactria, which per Zoroastrian scripture was the or one of the earliest center of conversion(s). The Helmand in Afghanistan is also frequently mentioned, and the Hamun Lake was (probably) thought to be the future birthplace of the Saoshyant (Bringer of benefit), the Zoroastrian Messiah, having preserved Zoroaster's seed to impregnate a virgin bathing in the lake.

What must have taken long time (though it is hard to know how long, probably sometime before the Achaemenid empire, but not everybody agrees) was for it to make its way to West Iran, i.e. Persia, Media, etc.

Is there any evidence that Iranian polytheists were assimilated directly into Buddhism or Hinduism rather than ever going through a Zoroastrian-phase in Afghanistan?

No, per the above, Afghanistan was converted early in the religion's lifetime.

To what degree did Zoroastrianism preserve Iranian/Persian polytheism?

The only sensible answer here would have to be "a very large degree". Old Iranian Religion was largely concerned with ritual veneration of divinities, and ones that personified both elements, and more abstract concepts relevant to the society those people lived in. Zoroastrianism preserves this in several ways:

• Zoroastrian divinities, most straightforwardly the six Amesha Spenta ("Holy Immortals") created by Ahuramazda, personify abstract concepts like Power, Truth, Health, et cetera. However, they are also associated with elements. To take one example, Khshathra Vairya, "Desireable Rulership", became associated first with with stone (and by extension the sky, which is a dome of stone in early Iranian cosmology), and later, with the advent of the Bronze Age, with metal. Or in other words, the tools of war.

• Furthermore, a broader category of divinities in Zoroastrianism, yazata (venerated things), includes elemental personifications, such as Atar, Fire, or Aban, Water, both of which have central roles in Zoroastrian rituals (and for this reason, these two are respectively tied to Ahuramazda and Apam Napat [a.k.a. Varuna], two of the members of the central Ahuric triad. The third is the well-known Mithra, who is associated with many different Yazata, sometimes fire, light and the sun.) In the way explained in the previous point, such yazata are generally also associated with one Amesha Spenta or other, often not in an entirely rigid way, much like how fire can be associated with both Mithra and Ahuramazda.

As you can see, the Zoroastrian "Pantheon" is complex and includes numerous overlapping categories (Ahura, Amesha, Yazata...) none of which translate straightforwardly to immediately familiar concepts of the divine in English. Theologically, it is ultimately the worship of the Amesha Spenta and the Ahura that grant humanity the boons and protections they need for spiritual warfare, but this must be carried out by observing proper ritual, which includes proper use of and respect toward the elements.

What do we know about Iranian polytheism that otherwise wasn't continued into Zoroastrianism?

Know is a strong word, but the single best indicator of this is probably the Zoroastrian Creed, Y 12:

I curse the Daevas. ... With reverence for Asha, and (offerings) offered up, I vow this: I shall nevermore damage or plunder the Mazda-worshipper settlements, even if I have to risk life and limb. ... 4. I reject the authority of the Daevas, the wicked, no-good, lawless, evil-knowing, the most druj-like of beings, the foulest of beings, the most damaging of beings. I reject the Daevas and their comrades, I reject the demons (yatu) and their comrades; I reject any who harm beings. I reject them with my thoughts, words, and deeds. I reject them publicly. Even as I reject the head (authorities), so too do I reject the hostile followers of the druj.

This is widely (and reasonably) interpreted as a relatively early pledge (possibly with later insertions) which converts from the old religion had to utter. This gives us a straightforward understanding as to what characterized the Daeva: they were amoral beings embodying destruction, killing and warfare. Or, as some would call it, martial virtues. But to Zoroastrians, amoral warfare embodied the wicked path chosen by Angra Mainyu (the spirit/idea of destruction), and proper rejection of them required not only abstaining from such acts, but also rejecting them in thought.

The suggestion made here is therefore that for Zoroaster, yazata (again, worshipped ones, or in relevant idiom, "all beings worthy of worship") could not only embody the physical and concrete, but had to also embody - be constrained by - an ethical dimension. To see indeed that explicitly amoral divinities were worshipped, we may turn to the Rigveda, in particular a conversation between Varuna (a member, remember, of the Ahuric triad in Zoroastrianism) and the god Indra, who in RV 4.42 stake out their claims to rulership:

Varuna: "Lordship belongs indeed to me, the eternal sovereign, as all the Amrta (Sanskrit equiv. of Amesha) acknowledge to us ... I let the dripping waters rise up, through rta [Sanskrit equivalent of the concept asha, loosely translating as "truth" but also "righteousness", "order", "obligation", etc] I uphold the sky ... Through rta I am the lord who rules through rta."

Indra: "Men who drive swiftly, having good horses, call on me when surrounded in battle. I provoke strife, I the mighty Indra. I whirl up the dust, my strength is overwhelming. All things I have done. No godlike power can check me, the unassailable. When draughts of soma [Avestan haoma, psychoactive substance of ritual importance], when songs have made me drunk, then both the unbounded regions grow afraid."

As we see, Indra seems to embody exactly this kind of amoral destruction. Indeed, in Vedic scriptures, "Deva" (equiv. of Daeva, literally "shining one", cognate of "divine") lacks a negative connotation (in Zoroastrianism, "demon" is a common approximate translation), and would eventually gain a positive one with Indra as the leader of the Deva. Sanskrit also has an equivalent of Ahura, "lord", namely Asura, though it is used in its literal, generic sense in the earliest layer of Vedic literature (so Indra and Varuna are both called "Asura") and it does not connote the exaltation that it does in Zoroastrianism.

From a material or societal point of view, it is easy to see how pastoral inhabitants of the Central Asian steppe would come to venerate amoral martial beings - many such societies historically have relied on raiding or extracting tribute both from each other and from more settled populations. "Mithra" can according to Boyce be traced to a root *mei, translating roughly as "exchange", "covenant" or "agreement" (referring perhaps to trade and similar practices, or covenants between tribes), whereas "Voruna" can translate as "Oath" (referring to more solemn vows relating to law, social hierarchy, etc). These then represented two types of interaction vital to the survival of such societies - trade, and commitment to social hierarchy. While the etymology of Indra is more heavily contested, it is clear how he would fit into this order in a society where plunder and tribute may at times have been economically (and socially!) important.

I hope what I have written isn't too confusing, it is very hard to explain the convoluted intricacies of Indo-Iranian religion!

Besides Boyce, I suggest looking at the Encyclopedia Iranica which has great articles with many references to primary and secondary sources, and I use it and its sources to check questions of etymology, attestations, etc.

If you have any followup questions I will be happy to take them!