Bonus question: I'm under the impression that early Christians were pacifists and that that annoyed the Roman government, so when Constantine has his dream to place crosses on shields to win a battle...wouldn't that seem odd to the Christians?
As for the status of Christianity at the time, from 303 onwards you have a series of serious edicts aimed at Christians throughout the empire. This included the destruction of Christian buildings, destruction of Scriptures, and a requirement that anyone appearing in court offer a sacrifice; this essentially barred Christians from the legal system and government office. Furthermore, governors were supposed to arrest and imprison bishops. Everyone throughout the empire was supposed to sacrifice.
Of course, local implementation of these edicts varied in intensity, severity, and thoroughness, but it was probably the most significant and systematic attempt to actively oppose Christians throughout the empire.
In 311 Galerius issued an edict of toleration, essentially repealing some of these measures. But toleration was an interim measure and I suppose you could say that the ‘status’ of Christianity during the 310s was a little up in the air. It wasn’t clear which way the political currents would go. Under Constantine in the west there was already toleration. The aftermath of Constantine’s victory was that Licinius extended the same toleration to the eastern provinces via the Edict of Milan in 313.
How shocking was Constantine’s conversion? I would venture not that shocking, but still surprising. We know that his father was tolerant of Christianity and his mother was a Christian. Likewise, his conversion should not necessarily be understood in terms of more recent sociological patterns of conversion. It is difficult to be certain what went on subjectively for Constantine. Certainly, although you see this later dramatic recounting of his vision and victory at the Milvian bridge in 312, you don’t see thorough-going changes to his policies and politics, you see gradual change and ‘Christianisation’ throughout his rule.
Christians as pacifists: Yes, you’re impression is generally correct. For the first three centuries the almost over-whelming witness of church documents is that military service was considered an inappropriate occupation, much like prostitution and acting. Converts from these fields were encouraged to find new employment, and in some cases supported by their community while they did so. Tertullian in particular writes about this.
It’s probable, however, that there were some Christians serving under Constantine in his military. During the 4th century you certainly begin to see a change, but most of it is post-Constantine’s conversion. That is linked with the demographic changes as Christianity goes from about 10% of the population around 310 to close to 50% by 350, and the high 90s by the end of the century. The change in the social position and role of Christianity in the Roman Empire places a number of social pressures on the religion and its practices and teaching, that are negotiated in different ways.
I suspect that Constantine’s soldiers put the Chi-Rho on their shields, if that account is taken as is, simply because they were told to do so. Soldiers who are loyal do what their commander tells them, and if Constantine told them he had a vision to do this and they would win, that’s exactly what they would do.