@Alex Zetsu
I think the fear was more that the colonist thought they were going to have a feudal/authoritarian system of government imposed on them, and an attempt was going to be made to turn Anglicanism back into something more Catholic - under the pretext of expanding Quebec.
Due to some PoD in which Quebec is subject to the Intolerable Acts, Quebec sends delegates to Philadelphia and signs the Declaration of Independence
Firstly, how does the subsequent war progress?
I don't know how Carleton makes out, but the hair on the back of his neck is probably standing on end. I think the Canadiens will be waiting to see how events unfold, but will be more neutral than OTL, so he will have almost no Canadien volunteers. He might skip out to Nova Scotia or Newfoundland early, but it is just as likely that he gets caught. Carleton seems like a level headed person that strove to maintain good relations with the Canadiens. So the Brits having him administer the area was beneficial for their cause, and his loss will be a great detriment.
As soon as word of Ft. St Jean falling reaches Quebec, that city will go for the Patriot cause. I would guess that the Canadien Patriots would raise 5 to 9 regiments. If the Patriots can scoot up to Nova Scotia quickly enough they can take over Halifax. This at the extreme of plausibility, and would require an earlier French (covert) intervention, or more success with the Boston Campaign. I don't think Halifax can be held against sea attack, so there will be a slog through Canada. The number of troops the British sent will push the Patriots back into New York so we could either have a big battle at Ticonderoga, or a repeat of Saratoga if the Patriots don't stumble in their strategic withdrawals. But the Patriots will have to send an army back into Canada to free it from the Brits. The upside is they wont have time to go genocide the neutral Iroquois. Maybe France can pull together a naval assault on Halifax, but I don't think it likely.
Secondly, how are talks over the forming of the U.S. impacted?
I think the Articles of Confederation get passed. At least the St. Lawrence River Watershed goes to the Patriots. I think ownership of Nova Scotia (& associated territories) will depend on local sentiment, and you might end up with Patriots leaving there as UEL come in. Rupert's Land, British Columbia, the Northwest Territory, and Newfoundland are staying British for now. I am not sure how ownership of Labrador, the Floridas, Bermuda, or the Bahamas works out. Getting Canada to give up their excess territorial claims will be more difficult than the New Englanders and Virginians I think.
Thirdly, how does this U.S. fare with Quebec included?
If a new constitution is ratified it will be looser, and more protective of individual state rights. I don't think Canada will care for the Quasi War, a War of 1812, or about the slavery debate at all. This Canada will likely support purchasing the Louisiana Territory, and support expanding further north and west. I think they will be ambivalent about an annexation of the Republic of Texas. I don't know how they would feel about the Mexican-American War, but I don't think they would support an invasion of a secessionist state.