Wow! There is a lot going on here in this first chart. Starting just prior to 1920 World War I kicked off - so it would make sense since there is a world war going on that immigration all over the world would decline dramatically. You can see that it leveled off for a brief period in the 1920's post World War I then decreased again. I think this would be related to the Great Depression in the United States. You see a steep increase post the Great Depression with Canada then during the Korean War - Canadian immigration dropped. During the 1960's despite the Cuban Missile Crisis and the advent of the Cold War with Russia and its satellite nations - sees an overall increase immigration from countries other than Russia or the "USSR" and its satellite nations. This appears to be due to a very large increase in economic prosperity during the post World War II era where the United States became a world industrial power exporting many goods to foreign countries.
You can see here the sharp increase in percapita GDP from around the world. This is also a sharp increase for the United States. It looks like the United States percapita GDP was greater than that of the others countries which explains why people would immigrant even though their countries percapital GDP is on the rise.
This is great! Life Expectancy in many countries appear to be on the rise. It seems that in the 1930's there was a sharp dip - possibly explained by a world recession connected to the Great Depression in the United States. It also makes sense that there was a sharp decline in the 1940's for life expectancy due to World War II. A lot of people died during this war in all countries so it only makes perfect sense that it would affect the life expectancies world-wide. It's interesting that there is also a decline in the 1960's and I believe this is due to the Vietnam War in which a lot of countries were involved in due to being allies with the United States and France. Post Vietnam Era it appears that life expectancy was on the rise.
It appears that for this period - world populations were on the rise - despite some wars. It looks like China and Brazil were growing the most which would explain immigration to the United States for these populations. Amongst the largest immigration populations are Ireland, Germany, Italy and Canada during this period - yet nothing points to the reason why? There must be something else going on that we don't see on these charts. Would need to do some further research by country to see what is going on.