While we're on religion, is there anything in particular that separates the non-Unitate Church from the Unitate Church aside from the obvious fact that one's in Communion with Rome but the other isn't?
The Non-Uniate Church is strongly dominated, though not outright controlled, by the ruler of Chernigov. There are various linguistic and theological differences. There is the filioque clause (Uniates added it, Non-Uniates haven't). All in all, over time, the Uniate Church has become very close to the Roman Catholic Church, being simply a privileged, autonomous branch with Greek Rite; the Non-Uniate Church is somewhat closer to (an idealised picture of) earlier Byzantine Orthodoxy plus various local weirdness like the two-fingered sign of the cross (not all that close to the OTL Old Believers in most other regards, though). Also, somewhat different pantheons of saints.
-What poor, poor Kronprinz? Please tell me he's had the decency to commit suicide. I WANT DETAILS
It's something of a taboo topic, and happened seven years ago... Mostly it was general debauchery, highly-dubious "friends", one of whom was, as it turned out, on a Danish payroll, Crowley-style occultism (actually, probably the source of the problems in this case) and, finally, a fatal overdose after which ignoring the elephant in the room became impossible. The current heir is much more decent, though, or so it seems.
For Dachs' edification, I forwarded that part of Masada's answered questions to Dachs, but none of the rest. I can send you the rest if you like, as Montferrat and the HRE are allied.
That's up to Masada, isn't it?
What caused the religious break between the Anglican and the Roman Catholic Church and what is the status of the schism now?
A religious "awakening" in Arcadia Proper plus the fall of England to the French in the 18th century which could not help but cause a crisis of identity. King Arthur III's meddling did not help. There have been various other disagreements over the past few centuries, but now they actually led to a complete break-off and the establishment of a state-controlled Anglican Church centered in Arcadia. It's not all that irreconcilably different in matters of organisation and theology with the modern Roman Catholic Church, but by now what differences there are have been fortified and an alternate, centralised ecclesiastical hierarchy has been established; politically, a reunion seems unlikely at the moment.
What is the religious composition of New Albion?
Highly mixed, what with the Asian immigrants; predominantly Roman Catholic, though.
How large is the influx of immigration from Europe and Mexica to Arcadia as compared to OTL at this time?
Not much from Mexico; as for Europe, I'd say proportionally it was much larger in the 18th century, given have many people fled during and in the aftermath of the Fifty Years War; on the other hand, it comparatively trickled down during the 19th century, though there have been occasional new waves, and overall the migrations are increasing again now in the aftermath of the crisis of Pax Germanica.
Is there yet a transcontinental North American railroad?
No.
What about the status of rails in general?
Steam trains, naturally. Most European nations and the Pax Germanica have their own railroad lines, connecting their most important cities at the least (Pax Germanica and Arcadia are more developed in this regard, though; France of all nations has been catching up). Also present in the more developed colonies; not as yet adapted in Japan despite some proposals; a minor railroad between the capital and an imperial residence in the countryside has been built in Xin Ming as something of a prototype.
Bannana Lee told me a good one but I forgot. 
