I doubt he had the vision too; he had, in fact, a long track record of having suitable visions at all the right moments (one of Apollo just a few years before), so I think visions were a propaganda device for him. But I do think he probably was a convinced Christian. There were still so few Christians in the Empire in c.310 that any kind of realpolitik reason makes no sense at all; hence it can really only have been conviction. And let's face it, Christian faith has never been a huge bar to unpleasant action.
I think it was definitively lost only from c.610. As late as the 590s Maurice's generals were campaigning in the area and reestablishing contact with Roman communities in the area. control had been lost temporarily before that, but always restored. The early seventh century collapse of the Danube frontier in the face of Avar/Slav attacks (early in the reign of Heraclius), with the need to fight off Persians and then Arabs in the East, proved definitive. But, of course, this is administrative/military control. Actual Roman life - villas, towns etc. - in the area had suffered a bit in the third century and then very heavily from 376 onwards.
I would estimate the situation to have been somewhere in between the 2 extremes you cite. My best guess as to Gothic numbers would be c.100,000 & the late Roman Iberian population was probably c.5 million if not a few more. So the genetic impact would not be huge, esp. since the Goths were not a genetically stable and distinct entity anyway. But I'm sure that words like 'choose' are wrong. If only 100,000 people, the Gothic army was c.20,000 at least, which was more than big enough to ensure that by the later 5th c. Hispano-Romans had no real choice over whether to accept Gothic domination or not. The sources make clear that the end of the Empire was a much more violent process than some euphemistic modern constructions want to pretend.
It's only really in the Vandal kingdom that religious conflict between Arians and Catholics figures very largely as a factor keeping Roman & barbarian apart. I think that's because the Vandal kingdom was the only one created while the Catholic western Roman Empire was still alive and kicking. All the other kingdoms emerged from the process of imperial collapse, so that there was no alternative Catholic Roman state for Catholic Churchmen to look to in opposition to their new Arian barbarian rulers. Hence they had to get on with the process of accommodation and clearly did. They used the Gospel text 'render unto Caesar' to justify this, sayihng that, since God had put the new rulers in power, then it was their job to work with them. And for the most part, Catholic Churchmen and Arian kings then got on together happily enough; Theoderic even solved a Papal succession dispute!
The most important thing has not been 1 find, but the important set of findings to emerge from many field surveys. BEtween them, these have made it clear that the fall of the western Empire in the fifth century was not simply the result of massive economic decline in the fourth, which is what had always been assumed. The fourth century was if anything a period of maximum population and agricultural activity. But, for a single find, I love the find from the banks of the Rhine of the booty from some barbarian raiders who were in turn ambushed by a Roman patrol: not a couple of necklaces, but 3/4 of a ton of looted metalwork in a couple of carts: the entire contents of a villa!
Citizenship still mattered in the late Empire because it meant that you were at least 'free' as opposed to a slave or colonus. I think citizenship as such ceased to matter as the successor states form, because status comes to be measured in a new way. The barbarian law-codes all posit a triple distinction in social status: free, freed (a permanent, heritable category), and slave. This is a non-Roman social categorisation, and former Romans were clearly realigned according to it. I suspect, however, that having Roman citizenship previously gave you a head start in securing the new, crucial free status.
It certainly was. We know from Origen's Contra Celsum that some pagan intellectuals were worrying about Christianity from the 3rd c, and you have to wonder whether the Neo-platonists emphasis on a type of monotheism was in some way a response. But certainly by the 4th c, Christian sensibilities influenced pagan ones against blood sacrifice. By the 370s Libanius is advocating a new sacrificeless pagan piety.
You'd probably get v. different answers from different historians. For me, studying economics, which I did briefly, has had the greatest external influence on my understanding of historical causation and the operations of human beings. As to the future, its not an area on which I'm at all expert, but I suspect that population modelling will play an increasingly prominent role in the study and understanding of early periods like the first millennium.
Who says it was declining? I actually see no evidence of it (see book). social structures were operating as solidly as they had ever done on the eve of the great barbarian invasions, and certainly economic structures, if not technology, were more fully developed than ever before. In my view, the Empire doesn't decline, the world around it changes...
In part, the pogrom was manipulated by Olympius who was seeking to replace Stilicho as effective ruler in the west. What gave Olympius the opportunity to succeed, I suspect, was the fact that Stilicho had drafted 13,000 former followers of Radagaisus into the Italian army just previously (in 406), and it was hostility and jealousy towards these newcomers from Roman regulars that O could exploit. I think, by the way, that recruits from the pogrom took Alaric's following up from 20,000 to 30,000; ie it added 10,000 - not 30,000 - men (the texts are unfortunately a bit dodgy here).