Immigration is not a problem, even in Europe. At current rates, it would take several generations for immigrants to make up half of the population. But at that point, the immigrants' children and grand-children will have assimilated. Just like how immigrants to the USA lost their native language and customs, so too will this generation.

Today, the only thing remaining from the influx of Italians, Irish, and Germans, are a bastardized holiday, canned raviolis, and maybe a few "heritage" festivals. Hell, the USA fought two major wars against Germany despite previously having a large influx of German immigrants.

On the other points, I absolutely agree. It's often cheaper to just buy nations than to deploy your military at take it by force.