Is it true that being in debt hurts your immigration potential? I don't really remember where I read it, so it may be an old version deal, but I try to avoid it.
I take the following approach to immigration, to be applied universally to all nations to achieve maximum immigrant output:
1)As said before, liberalize and raise plurality as much as possible, build factories/ensure RGO's have available jobs, raise services (except the ones that hurt economy, ick).
Party policy seems to affect the immigration, they like atheist/full citizenship policies the most.
2)I tend to use the scripted revolution events to turn the USA reactionary; this basically cuts off all US immigration and diverts it to the rest of the World.
3)Save my game and load it up as Germany, Russia, China, France, Japan; make them monarchies and randomly jump from party to party to raise their militancy. This will see a tremendous exodus from their countries to my nation, or at least allow me to see what nations are competing with me for immigrants.
4) Load up any nations who are stealing my immigrants (usually some random SA nation) and turn it reactionary.
From there on, you should be rolling in immigrants, and they will typically move wherever the latest factory is being built. As such, I try to concentrate factories in one province (harder in Revolutions, obviously) to reduce their confusion.
On colonial immigration and immigration within states: As said, you need to load up RGO's (5/5, 10/10) to the point where there are unemployed farmers and minors sitting around. They'll try finding work in whatever colony they madly decide to move to (it has to do with resources, gold and the like, sometimes at least. I don't know how much method there is to their madness in all honesty). They'll keep going to the same state(s) until you grant them statehood, at which point the appeal magically disappears.
Within your nation itself, POPs will move wherever the latest factory has been built, including farmers for some reason (or at least they used to in vanilla vicky). Go figure.
EDIT: On assimilation; America basically assimilates all POPs, including natives who were there no matter who (including mexico and canada) so long as Yankees are 50.1% of the population. Though you said certain groups of more than 10,000 may be resistant to assimilation, as is the case with other nations, America seems to assimilate them regardless.
I had a game where I, without cheating, Yankified all of North America and the Carribean 100%, simply by getting yankees to 50.1% everywhere by virtue of immigration and the occasional genocide.
It also seems like POPs with a different state religion won't assimilate unless you have atheist (and maybe secular) party policy. Not 100% on that though.