Newfoundland and the Hudson Bay Company areas are out of reach of the Patriots. There was some interest in detaching Nova Scotia from the Empire, and there was the invasion of Quebec. The British are not going to try to claim what became Ontario if the Patriots both successfully invade Quebec and hold it against any counter attacks.
None of this affects what became British Columbia. Also, IOTL the British had a very small garrison in Quebec, but heavily reinforced it, and the reinforcements became the basis for Burgoyne's army. If they lose Quebec city in 1775 or early 1776, and don't try to retake it, those reinforcements go someplace else. This still changes the course of the war, and the Treaty of Paris will be changed in other ways. The British may wind up keeping a few southern colonies.
A USA that has conquered Quebec can integrate it fine. They had no problems with New York, which was still half Dutch. They managed with New Orleans and Hawaii later. Catholicism would be a problem, but the USA absorbed a ton of Catholic immigrants.
Quebec, Nova Scotia, and New Brunswick become states. I'm not sure about Prince Edward Island. The area between the Ottawa River and the Rockies is divided up into territories and later states. None of these will be slave states, so you have a situation where there are more free states than slave states well before the Missouri compromise. This starts producing butterflies affecting early 19th century politics very early.
The War of 1812 is butterflied away. The only reason to fight it is the impressment issue, which was actually settled diplomatically before the war. There is a very good chance the Mexican-American war is butterflied as well. Slave states don't have as much influence within the wider USA ITTL, so that goes differently. Some slave states may secede earlier, and the rest of the country, which now includes most of Canada, does nothing to stop them. Some might accept that that slavery is out of place in a wider confederation, and abolish slavery itself state by state, slowly, only asking for some sort of compensation from the federal government.
The parts of what are now Canada obviously get Amercanized, even Quebec to some extent, with the institutional and cultural British influence just not being there. Immigration patters will also change.