the number for foreigners for the skilled worker program Quebec has their own so you to do it through them and not through the federal government. So is there something like that for actual Canadian citizens to? I imagine they don't want a bunch of English-speaking people influx into their territory shifting the demographics
1. Quebec determine and choose Economic Immigrant on its own. They set their own target and method, hence why people need CSQ to immigrate to Canada when they are in Quebec. This is also why you cannot apply for federal immigration programs (EE for example) when you are in Quebec.
2. Any temporary worker and foreign student admitted to Quebec, needs the Quebec government's consent. This is why you need CAQ before applying Student Permit or Work permit, though usually, it's not a problem, just extra paperwork.
3. As for permanent residents and citizens, they can live wherever they want in Canada, including Quebec. Quebec government cannot control that per se. However, there are numerous policies in order to entrench French to Quebec society.