emigrate-leaving a country for good
immigrate- enter a country for good
...otherwise its just a temp resident, resident alien, or tourist.
If youre asking me to weigh in on the rest...
Governments should and have the right to lay any manner of entry restriction they wish. If such restrictions become too burdensome, that country will see a marked dropoff in entrants across all walks of life and see a corresponding drop in the excellent members of humanity as well as the bad ones. It will eventually cause its own leveling. If it is too harsh, it will be lifted in time. Hard restrictions are their own punishments in and of themselves. Noone is forced to travel to other countries... so putting up with another countries entry hassles are purely by choice. I've never heard of civil rights protections extending across foreign borders. New country, new rules.
Someone born in Brazil that became a resident alien of Canada and evntually a nationalized citizen? That one is a bit fuzzy in my eyes. I think that so long as the immigration happend before say the age of 12 then I would be cool in calling the individual a Canadian. Anything past that and you start to deal with ever increasing level of old national identity and split loyalties. There are no cut and dried answers and no real way to play group A one way and group B another way. Either make it all a hassle or lighten up.