In the Eastern Empire christianism probably spread easily, as it was essentially an urban religion (it was no accident that Augustine's ideal was the city of God), and fitted quite well into the evolving philosophical traditions of the empire. But in the west, were cities collapsed after the 5th century, I also believe that it spread though the ruler classes and due to its prestige by association with the customs of the old Empire.
Yes, I think all this is quite right. It is no accident that there were
very few non-urban areas in the Roman world that had a large proportion of Christians before the fifth century or thereabouts (the Berbers were a rare exception). Roman culture itself spread via cities, and Christianity basically piggybacked on that.
I very much doubt that the peasants who made up the majority of the population had any understating about the ideas of christianity, or even followed its rituals. Bishops were still quite busy stamping out traces of pagan rituals by the 10th-13th centuries, and likely didn't care about those at all before that.
I'm not so convinced by that. You must bear in mind that the distinction between Christian rituals on the one hand, and pagan ones on the other, together with the notion that there is fundamental incompatibility between them, is a way of thinking that developed in later Christianity (I mean post-fourth century) and developed slowly and at different speeds in different places. So the fact that what we think of as "pagan rituals" persisted for many centuries in certain places is not, in itself, evidence that those people were not thoroughly Christianised; they might have been thoroughly Christianised but have seen no reason to stop practising their traditional rituals (just as there are plenty of Chinese Christians who are perfectly devout but who still venerate Confucius and their ancestors).
And the rural areas of Europe were targeted by very intense missionary activity during the 16th-17th centuries again, because even then those populations didn't really knew the precepts of whatever christian religion happened to control their area (the era of the religious wars).
Surely these missionaries were not educating people about Christianity who didn't know much about it, but bolstering their faith against rival versions of Christianity or seeking converts from rival versions? I mean, this was about Catholics/Lutherans/Reformed versus each other, rather than Christians versus pagans. Although I don't know much about this period.
As far as the slow development of persecution by Christianity is concerned, that's a matter of point of view. Heresy has always been frowned upon - although it could only be declared so when a certain brand of Christianity was the dominant religion.
It's perfectly possible for one bunch of Christians to call another bunch heretical even when Christians as a whole are a small minority; the church was happily doing this from the first century onwards, even when its members represented less than one per cent of the empire's population.
Pagan religions, being polytheistic, had little cause for persecuting Christians - the major exception ofcourse being the Roman Empire and an important reason for persecution might very well be the refusal to recognize the deity of the emperor. But even so, persecution of Christians was never excuted systematically and never as thorough as when Christendom acquired a taste for it...
No! The Roman Empire was certainly not the "major exception" here. In fact Christians in antiquity were persecuted not only by the Roman Empire but also by the Visigoths (Athanaric, whom I mentioned before, was a notable persecutor of Christians), by the Armenians (Tiridates III persecuted the Christians before converting himself), and above all by the Persians. The persecutions of Christians in the Roman Empire were absolutely dwarfed by the incredibly cruel persecutions they suffered at the hands of the Sassanids in the fourth and fifth centuries. Shapur II and Ardashir II slaughtered enormous numbers, eschewing the legal procedures followed by the Romans in favour of simply ordering wholesale massacres in Christian areas, in which many non-Christians also died. For some victims they used particularly inventive forms of execution, such as dismemberment over the course of several days, being eaten alive by rats, or trampled by elephants. Even after Christianity was decriminalised in AD 410, there were still terrible massacres, most notably under Yazdgerd II in the 440s and 50s, in which tens of thousands of people died, almost certainly more than died in all the Roman persecutions put together.
Compared to the Eastern Empire, the Western Roman Christians never were particularly concerned with the orthodoxy of the belief as opposed to the purity of the clergymen who administered the sacraments and so forth. Donatism and Pelagianism both arose over this issue, and they were the major heretical beliefs in the region for the first several centuries of Christian dominance - outside of Arianism, an Eastern Empire invention that in the West was mostly confined to the Germanic peoples that came in and settled, and within two centuries of that settlement was basically gone as well.
You're right about Donatism (although that was almost completely confined to Africa) but not about Pelagianism: that was, initially, an ethically-motivated movement (Pelagius objected to people using original sin as an excuse for lax behaviour) but in the hands of Julian of Eclanum and the "semi-Pelagians" such as Faustus of Riez it transformed into a more philosophically, doctrinally inclined movement which was concerned with the nature of the will and of divine grace. Pelagianism was never about the purity of the priesthood. Also, don't forget the major disputes in the ancient west about Sabellianism and other Trinitarian matters, and then in the early Middle Ages about predestination, the nature of the sacraments, and adoptionism. So to suggest that western Christians were primarily concerned about correct practice and not correct doctrine isn't really true, I think. They were concerned about
different issues from eastern Christians, to a considerable extent, but not necessarily less dogmatic ones. Plus of course there were eastern controversies that revolved around practical rather than primarily dogmatic matters, such as Messalianism and, much later, the row over hesychasm.