1) How would Quebec fit into the union? Would there be a large amount of cultural tensions between it and the rest of the US? Would Quebec seccessionism in the 19th century be a possibility, and is there any chance of Quebec and Southern seccessionists forming some kind of tactical alliance? (ie, they both want to leave the US, but for different reasons).
Quebec would fit in the Union quite cozily after a while. The early US Constitution would have given it an overwhelming amount of autonomy and full civil and political rights for French-speaking Catholic, pretty much all they could wish for. At the Consitutional Convention, its representatives would have lobbied for, and got, clauses that guarantee its church (i.e. no ban for state-established churches) and its language (i.e. ban of a national language), but otherwise, they would have behaved much like the other big states. Politically, they would initially lean towards the other agrarian states of the South. As Middle Canada industrializes and the economic ties with New England, New York, and the MidWest grow, however, it would lean more and more towards the rest of the North. In due time, OTL Quebec would become a Catholic-Romance close copy of New England-New York, and OTL Ontario of the Mid West.
ARW Quebec is very likely to split into OTL Quebec, a Southern Ontario state, and a Northern Ontario state. Canadian states would lobby to have infrastructures built that enhance their ties with the WASP North on one side, and that allow swift colonization of western Canada on the other side, after it becomes US, which is all but inevitable, either by conquest or by peaceful purchase. The British Empire would not have any serious hope of holding onto Rupert's Land and Columbia, military, economically, or demographically, if America holds Middle Canada and the Maritimes and becomes stronger and stronger as time goes by.
Quebec secessionism by the time the ACW becomes likely would be utterly ASB: by that time, Canadian states would have become thoroughly integrated economically and politically within the North, just like the Mid West, and they would have no reason whatsoever to feel any sympathy for the slaveocracy. Montreal would have as many reasons to secede as Chicago.
2) Assuming Quebec doesn't leave, would America's sense of itself be affected by the fact that part of it is very different, culturally and religiously, from the rest of it?
A very likely butterfly is that there would be less prejudice against admitting territories with Catholic-Romance majorities. Hence, it becomes rather more likely that areas like (northern) Mexico, Cuba, and the Dominican Republic are successfully annexed during the 19th century.
3) Where would the loyalists go?
Outside North America entirely. Rupert's Land is far too remote, wild, and strategically unsafe to be a worthwhile resettlement area for them in 1783. They would be resettled in other British colonies: Australia and Ireland are possibilities. Alternatively, or it addition, Britain could pursue the conquest of South Africa and Rio de la Plata earlier and with more efficiency and determination.
And who settles *Ontario in their absence-Quebec or the Anglophone US?
Like the rest of American Canada, it would be settled by a mix of Quebecois, Anglophone settlers, and European immigrants. A west-east gradient is likely, with eastern Canada being more Francophone and western Canada more linguistically mixed. Nonetheless, Francophones would be more spread out than in OTL Canada.
4) Would the various parts of *Canada be tied economically to each other as much as OTL? In particular, would be see anything like the Canadian Pacific railway?
It is quite likely that Middle Canada states successfully lobby for an ATL equivalent of Canadian Pacific railway. To a degree, those lobbies would strive to build up western Canada as part of "their" regional power bloc. However, the various parts of Canada would also integrate with their economic matches south of the OTL border: the Maritimes with New England, Quebec with New Work, Ontario with the Mid West, the prairies and the Rockies, Columbia with Oregon and Washington. It would be a mix of west-east and north-south ties.
5) How would having Canada's resources and population affect the economic and political development of the US?
The ACW would likely occur somewhat earlier, say 5-10 years earlier, but not radically so. The economic and political weight of the free Canadian states would make the South feel cornered earlier. However, before resorting to secession, the South would push ever more forcefully than OTL for agrarian imperialism in Mexico, Central America, and the Caribbean. Canadian natural resources and population and the rest of the Union would humor them. This is another reason why presence of Canada would make America bigger southward. Canada would fill up more quickly ITTL, thanks to US immigration policies and more aggressive settlement and its extra resources and ppopulation would make America achieve superpower status somewhat more quickly, but not radically so.
); New Caledonia, today, has about 220.000 (or 300) people depending on how south its borders go: it didn't include Vancouver island and the southern districts obviously but I'm not sure for the rest.
