On the second point, when you say Abbasid crisis, you refer to the Abbasid Revolution, right?
I was referring to the IXth/Xth centuries crises, rather. Eventually Arabo-Islamic economical network wasn't really this much harmed by the Umayyad overthrow (the biggest losses were in the Islamic West, Ifriqiya, Maghrib and al-Andalus, which weren't really cores and largely autonomous already).
The problem rather comes from the mid-term consequences of Abbasid takeover, namely political consequences : sh'ia revolts, loss of more peripheral and economically relevant regions as Persia and Egypt, political-religious troubles culminating with Zanj revolt (which did a number, at least for a time, on plantation economy) and generally all of this being a financial drain.
Note that it's not really something specific to Abbasids, as Umayyad Spain suffered something similar (and with decline of peninsular silver mines) or Tulunid Egypt.
As a result of political instability, you ended up with inflation, productive decline,fiscal drain (both from central authority and officials), budgetary issues leading to government taking significantly more than redistributing not only directly but indirectly as well (such as the lack of great works)
Generally speaking, the Xth century wasn't that a good period for the cores of the Arabo-Islamic world, altough not catastrophic (a comparison with the late crises of Romania could be made there)
I would rather consider Buyid's takeover to have really put thing backs in order, but Abbasids themselves weren't blind to the issues and tried resolving these, with partial success, and Buyid's generalisation of iqta had, while stabilizing effects, long-term consequences.
Anyway this crisis was felt in Scandinavia for obvious reasons, but as well in western Europe generally (products from eastern Mediterranean basin became rare or virtually absent in the late IXth and Xth centuries, while present during the VIIIth/IXth centuries). Again comparing two different events, there was something similar with the contraction of Roman presence in Latin Europe by the late VIIth/VIIIth centuries due to costly Romano-Persian wars and Arab conquests, which really dynamised already blossoming North Sea trade.
Well, it is certainly true that there were strong factors encouraging the adoption of Christianity thanks to its presence as an organized religious institution.
Its close association with prestigious and relatively strong political model was certainly another factor.
However, a more organized Scandinavia doesn't necessarily have to mean an end to foreign military interventions, or to a widespread system of trade.
I think it does mean that a bit, tough : while you're right pointing out Christianisation didn't meant immediate or short-term halt to raids, but it's quite implicit IMO that Christianisation meant integration of these polities within a normative network of political and economical exchanges (not just for Scandinavians, but Slavs and Hungarians as well). The sheer economical/cultural gravity of Eur
We cope at this point makes systemic alternatives quite difficult.
Most definitions of the Viking Age continue after the conversion to Christianity. For example, no one excludes the Christian kings of Olaf Tryggvason, Sweyn Forkbeard, Canute the Great, or Harald Hardrada from the Viking Age.
I saw arguments about how Knut and Harald Hardada as the end of Viking Age, and the beggining of active integration of Scandinavian polities in Europe, for various reasons : royal campainging instead of autonomous "guilds" and nobles, objectives being less raids than imposing political and fiscal authority, etc.
Nobody denies, of course, there is a direct continuation but as arbitrary divisions goes, putting it before Sven Forkbeard makes more sense than afterwards IMO. That said, it's not perfect, because Olaf Tryggvason rather wells fit the Viking Age model.
Long story short, I don't think Christianisation changed practices for itself (Haakon of Norway is quite interesting on this regard), but Christianisation tended to imply geopolitical changes of perception eventually.
You could argue that if Norway could have reclaimed Northumbria after the mid Xth century, the distinction on this regard could have been more blur : again, it's essentially about arbitrary division for me there.
We can also look to the expedition of Ingvar the Far-Travelled, one of the most far-flung "non-monarchical" Viking raids well into the era of Christianization. (Of course, Ingvar's raid itself could reveal recognition of economic crisis, with attempts to establish new trade links after the collapse of the Khazars.)
I do think that's a better exemple, to be honest. That being said, early Sweden was still in a stituation of political division at this point, knowing a more slow evolution than Danemark (which own unification might have been delayed by the IXth century) and Norway. It's understable that the political/cultural changes felt elsewhere didn't there : I don't think we can consider this "well into the era of Christianisation", but rather at this beggining in Sweden.
Whoever managed to rule in Eastern Europe wouldn't want their coast plundered... but much of this coastal area wasn't Christian anyway.
Which is really besides the point (to be honest, I don't know why you say this) : what I said was, in the case of an earlier state-building in modern Poland (I mentioned, rather than Vistulians or Veleti, Pomeranians managing to form a strong complex chiefdom), whoever would rule there wouldn't just accept Viking takeover, and that their predominance on the region wouldn't be peaceful. That's all (even if I think that, ITTL, you'd have probably the baptism of one or two Pomeranian dukes/kings as it happened with Veleti and Vistulians, but nothing leading to an earlier Christianisation as in these exemples).
But in face of this instability, I wonder if one of the rebellious factions such as the Buyids could have been more successful, and despite originating as an usurping faction responsible for the Abbasids' decline, could have then created a new "stability" quickly enough to revive economic development.
As said above, I agree that Buyids may have represented a factor of stabilisation in Iraq. But this was in the late Xth century, while Abbasid decline was significantly more advanced than in the IXth century. I agree with
@John7755 يوحنا there that Samanids weren't really a threat for Abbasids, being rather focused on the eastern periphery.
We could argue that the unability of the Abbasids to take down Tulunids could accelerate their demise, not in the sense that it would change much economically (Fatimid takeover happened really quick, altough ITTL, Abbasids could loose more of Syria as well) but as a moral defeat and hasten things.
But maybe it would be better to preserve Abbasids hegemont in Near-East : we could , as proposed by John, crushing Qarmatians as soon as possible to give Abbasid some breathing space. Or even prevent Fatimid takeover of Egypt which might be more interesting (while difficult).
Here's why ; let's imagine Umayyads are unable ITTL to restore order to a significantly crippled Muslim Spain (there were muladi, berber, arab, urban, christian revoltees more or less everywhere). Conversly, Egypt is less interesting and ripe for the taking than IOTL because...reasons (this is the main difficulty, to be honest, and not easy to resolve).
al-Maghrib being a mess of various tribes, states, factions and different affiliations, often under Umayyad influence IOTL, and pro-Fatimid faction never managed to take the lead durably (places switched hands on a 10 to 20 year basis). Umayyads being unable to intervene as much as they did IOTL in the region; and you have to make Morroco somewhat interesting enough for Fatimids that they clientelize (I dare not say outright conquer, but a partial conquest will be needed) the various Berber kingdoms.
al-Andalus is relatively easier. Some rebels as Ibn Hafsun did pledged alliegance to Fatimids IOTL, so some muladi support to a Fatimid conquest could work. And giving that preventing Ummayad revival in Spain would likely end up with an earlier Christian advance (which in turn could be something strengthening Christian principalties on the other side of the Pyrenees, including against Vikings, you can't have your cake and eating it), but Fatimids could pull an Alomhad while taking the whole lead on Islamic West.
This should give Abbasid enough breathing space in Near-East, without Qarmatian revolutionnaries and Fatimid patronage and alliance.
That being said, I don't think it would lead to a much prolonged Viking Age in the Atlantic, and while possibly so in Eastern Europe, I could rather see Volga Bulgaria and possibly Khazars being strengthened by a renewed stability in Iraq, so that's not even a given for this region.
Very good point. Also, many scholars argue that Canute the Great didn't actually intend to form a lasting united North Sea Empire or create it as an institution. I think his successors though, potentially might have been more motivated to do so, as they were then reuniting a former empire in recent memory.
I think the key there is the nature of Scandinavian kingship that tended to consider that titles to be inherited as a same package : if the kingship of Norway was at some point associated with the kingship of England or Danemark, then both were tied up and ground enough for claiming re-uniting them on a personal level.