If the Arabs hadn't been ready and willing as a culture to put aside (some) of their tribal differences and spiritual traditions in order to assume a greater place in the world, then Muhammed wouldn't have been able to unite them in the first place. The most important part of Muhammed's teachings in the immediately practical sense was to create a fairly clear idea of succession; without that, the Arabs are leaderless after his death but still looking for their place in the sun. Of course, now "their place in the sun" doesn't have to mean or imply "spreading the light of Islam to the entire world".
And they're getting it soon enough. Islam didn't topple the Sassanid empire, the Sassanids managed to do that to themselves through amazing selfishness, incompetence and outright madness in their ruling class. Add the occasional general who came up through the ranks and can see just how screwed up the state is with something like an outsider's perspective, and hilarity ensues. So the Sassanids collapse on schedule; no outsider was expecting this, but Byzantium is bureaucratic, frequently fractious and nearly bankrupt from its recent wars with the Sassanids while the Arabs are able to respond relatively quickly. They graft themselves onto the wreckage of Persia and become its new ruling class, stitching the Empire back together more or less. They have no reason not to adopt Zoroastrianism, Persian culture and perhaps even Persian language, so very soon the different ethnicity of the new ruling class will mean nothing at all. Since they don't have to take over the whole world, though, expansion into Egypt will seem like more trouble than it's worth in the short term, as will the Battle of the Talas River - so papermaking doesn't find its way to the West on schedule.
I have to disagree with some of your points - given the right circumstances, it is actually far more likely that the Arabs take over Egypt than that they manage to conquer the Persian heartland.
The majority of the Egyptians and Syrians were Miaphysites who were more or less persecuted by the Byzantine authorities, and thanks to the fact that the recently ended Sassanid occupation lasted so long that so long that an entire generation grew up under Sassanid rule, the majority of the Syrians and Egyptians won't have much love or affinity for the Byzantines.
It is far more likely that the Egyptians and Syrians will accept the foreign and "barbaric" Arab invaders as overlords than that the Persian and almost entirely Zoroastrian population of Persia proper submits those same Arabs.
But if they
do pull off a successful conquest of Persia itself (which is admittedly still in the realm of possebility), then it is, as you say, rather likely that the Arabs will adopt the Zoroastrian religion (this way, they might also gain the support from the powerful Zoroastrian priestly class), and they will certainly adopt the Persian language and culture (this happened even in OTL).
However, I do not think that the differences between the Persians and the Arab ruling elite will ever disappear or stop being important, regardless of how much the Arab ruling elite assimilates.
In this scenario, it is far more likely that the position of the Arabs in Persia becomes similar to the position of the Mongols in Yuan dynasty China; an empire ruled by a strongly assimilated elite that is still regarded as foreign by the native population.
..
As for the spread of papermaking into the Middle East and the West; this is indeed likely to be delayed for a bit ITTL, but I really don't think that the absence of the Battle of Talas will have much - if anything - to do with that.
The OTL Sogdians were already quite familiar with Chinese paper, and regarding the fact that they frequently used paper alongside parchment even before the Muslims conquered Sogdiana, it is not unreasonable to assume that the procedure of papermaking was already known to them even before the OTL Battle of Talas.
In fact, I'd even dare go so far as to say that the OTL Battle of Talas may have had nothing to do with the actual spread of papermaking to the Middle East, that the Muslims adopted the procedure from the Sogdians rather than directly from the Chinese, and that the story of the papermaking Chinese prisoners of war is a mere legend.
What's more; with a weak Persia, the Tang will expand their influence into western Central Asia just like in OTL, and if the Persians don't make a strong comeback during the 8th or 9th centuries, then Chinese influence in western Central Asia could actually last significantly longer than it did in OTL.
And that would in its turn result in more Chinese influence in the West, or at least western Asia, and it could very well affect the spread of the procedure of papermaking.
However - exactly how long the procedure of papermaking will spread to the West ITTL depends on how fast paper will be adopted by the Byzantines. ITTL, Byzantium is essentially the only 'eastern' polity that has any real influence in the West.
Hispania, though, is going to stay Arian and acknowledge the Synod of Toledo as its fount of spiritual authority, not Rome. Rome will try debate, bribery, and a variety of emotional appeals, which will all fail. The question becomes, when will Rome have the muscle to try to bring Hispania into the fold when words have failed? Perhaps this is the first crusade.
Wait, what?
Arians have
never been a majority in Spain, and Arianism largely remained restricted to the Gothic ruling elite.
Even
if the Gothic elite would remain Arian, which didn't happen in OTL and won't happen ITTL either (the conversion of the Visigoths happened decades before the Muslim invasion - keeping the Visigoths Arian would require a secondary POD), they'd still remain a minority ruling over a Catholic and essentially Roman majority.
You may believe that butterflies prevent Leo the Syrian (Isaurian?) from coming into existence, but I prefer to think that he or someone like him will arrive on schedule. Having demostrated his cunning and ruthlessness on the frontier against the Persians, in OTL there was nothing for it but to promote him to the capital; here, there's a much more suitable (and safer) place for the Emperor to put Leo - the surviving Exarchate of Carthage. Once he has that degree of autonomy, his iconoclastic streak comes out, and after a few years of careful preparation, his ultimatums to Byzantium predictably ignored, he declares the Exarchate sovereign and wins a war of independence. Eventually, Egypt will follow suit - it, too, is overwhelmingly iconoclastic, and now it has a sovereign iconoclastic kingdom neighboring it which may offer (sincerely or not) support in rebellion.
To my knowledge, the Iconoclast movement was largely a result of interaction with and influence from Islam, and I do not know of any iconoclastic sentiments, let alone an iconoclast controversy, among the Christians in Egypt.
With no Islam, the Turks will still migrate into Imperial territory, but now they will certainly convert to Orthodox Christianity, and attempt to assimilate into Imperial culture.
I see that you're kinda overlooking the developments in Central Asia, which is not a smart thing to do when trying to predict the migration patterns of the Turks...
ITTL it is quite likely that the Turks come under significant Nestorian influence, as Nestorianism was already fairly well established in Central Asia during the 7th and 8th centuries. And with no Islamic expansion into Central Asia (no Islam, no Samanids, et al), it is not unlikely that we'll see a number of Nestorian Turkic khanates and principalities pop up.
Exactly how successful Nestorian Christianity will be ITTL depends on the circumstances, but it certainly will be one of the major religions in Central Asia.
A successful Turkic invasion of the Middle East could still happen, though TTLs Turkic invasions will propably be very different from their OTL counterparts - and not in the least place due to the fact that the Turkic states ITTL will be very different.
For example; there is no guarantee that there will be an equivalent of the OTL Great Seljuk Empire ITTL (there's quite a difference between the occasional raid into the Khoresan, and a wholesale conquest of Persia, Mesopotamia, Anatolia and the Levant, after all), and likewise, it is
extremely unlikely that something like the Battle of Mantzikert will happen ITTL, as this battle and its aftermath were the result of a very complex and peculiar set of circumstances.