Throughout most of our history, immigrants had a higher education level than most Americans. That is no longer the case.
The second claim hits closer to the mark, and is the reason we aren't handling assimilation well. Why should anyone want to assimilate into a despicable society, or at any rate one portrayed as such by its leaders?
They are not assimilating for a number of reasons. First, once you have a critical mass of numbers, you don't have to assimilate, especially when you can easily maintain daily contact with your home country and can still maintain familial ties.
Second, we have taught immigrants, the vast majority of whom are minorities, that there are benefits to being a minority and retaining that identity. Affirmative action and minority business set asides reward those who believe that they are victims. There are tangible benefits to retaining one's "tribal" identity.
Finally, they are not assimilating because they don't share the same sense of connection with our Founding Fathers who were white and Western European. They are associated with the same kinds of people that established colonies and dominance over minorities. For many who come from Latin America and Asia, white Europeans were not benign benefactors.
The U.S. adds one international migrant (net) every 36 seconds. Immigrants account for one in 8 U.S. residents, the highest level in more than 80 years. In 1970 it was one in 21; in 1980 it was one in 16; and in 1990 it was one in 13. In a decade, it will be one in 7, the highest level in our history. And by 2050, one in 5 residents of the U.S. will be foreign-born.
Currently, 1.6 million legal and illegal immigrants settle in the country each year; 350,000 immigrants leave each year, resulting in net immigration of 1.25 million. Since 1970, the U.S. population has increased from 203 million to 310 million, i.e., over 100 million. In the next 40 years, the population will increase by 130 million. Three-quarters of the increase in our population since 1970 and the projected increase will be the result of immigration. The U.S., the worlds third most populous nation, has the highest annual rate of population growth of any major developed country in the world, i.e., 0.963% (2011 estimate), principally due to immigration.
Demography is destiny. The US is not immune to the forces that have taken down other great nations and civilizations.
I seriously doubt this claim.
The massive influx of Irish in the early/mid 19th century was not composed of well-educated professional people, nor the huge numbers of Italian peasants coming in in the late 19th and early 20th centuries. The Chinese "coolies" of the second half of the 19th were not educated. To quote only three examples.
To be fair, of course, education was not nearly as critical to life success back then.
To address your other issues, it is probable that we assimilated the Jews, Italians and others that came in such huge number pre-WWI is probably because there was a decades-long moratorium on immigration, cutting them off, as you say, from fresh blood. No choice but to assimilate.
But I still firmly believe that the real issue is ideological. Immigrants are taught by our media that "their" culture is one to take pride in, and that "our" culture is one to be ashamed of. Why would anyone want to assimilate from a culture to be proud of into one they would need to be ashamed of?