On Western Europe:
Im not talking about the rest of the world or Western Europe but the United States as the OP is talking about North America. In my opinion, obesity among women and anglo-feminism are the main problems in the United States and not immigration. There is plenty of evidence that immigration to Western Europe skews male, no doubt, which long term is not good demographically for Europe.
Despite that, Western Europe and even immigrant infested France and Germany are much better for any American male; just ask anyone whose been there. (Including myself
If you look at "Western" European countries with very little immigration such as Portugal, Scotland and Finland and you'll be looking at the ugliest women in all of Europe. (outside England of course). I have no explanation for that.
The same first article that I linked to also shows that immigration to the United States from Western Europe, Asia, South America (i.e. countries that we often travel too to fuck women) skews FEMALE.
On Immigration to the US:
Yes its very true that immigrant males 20-29 outnumber females.
Here are the actual figures
20-24 Immigrant Males: 52.8% pop: 1,250,000. Native Born: 51.2% pop 10,319,000.
25-29 Immigrant Males: 51.8% pop: 1,803,000 Native Born: 50.4% pop 9,487,000
However, that second link (Age-Sex Pyramids of U.S. Immigrant and Native-Born Populations, 1970-Present) shows that this number is ONLY (Im rounding) about 400,000. 400,000 over a 20-29 pop of close to 40-45 million is not that significant when you consider that males still largely make up the overwhelming majority of the military and prison populations.
To speak to the rest of your points, Im not sure what slim 30 yr old women are getting 2000 messages, it hasn't been difficult to date slim 30 yr olds in the US, sure can be hard to keep one down (even at that age).
On EE:
Lucky for me, I've also traveled to many Eastern Europe countries. There is no doubt a favorable ratio for males. This is backed up statistically as well. This is not due to lack of immigration however, but more due to long term trends from the past(the male to female in EE is at an all-time high since WW2 despite still not having any immigrants), early deaths, and immigration to Western European countries.
Values in those countries also favor males. Even though women are in the workforce and have equal rights. There is no feminism in Eastern Europe. Even with that women in EE (outside of Russia, Ukraine, Belarus) still get married and have children later then American women. This is all despite numbers leaning in the favor of males.
Separate topic:
This is a completely separate topic but I'm going to mention it anyway.
Im not sure having a society that is largely female like EE is good thing either long term. I remember being in Riga, Latvia a few months ago. I've never seen so many old people in my life. Over 65 women outnumber males by a 2 to 1 ratio. This number must have some negative effects. (im sure im unaware of)
Old women, while we want to take care them, are the most unproductive people on the planet. And to care of them, we want them to enter marriages when they're younger, not through a welfare state being paid for by 20 year old males and new immigrants.