About open borders and allowing immigration.

First, living "on top of each other" is great.  The condo provides all sorts of things and services people otherwise have to get themselves, manage themselves, and drive somewhere to obtain.   It is also ecologically much better.  That said, overcrowding applied to the US is a silly notion -- the States is a big underpopulated country with plenty of room for sprawling suburbs if that is what you really want.

Allowing free immigration is great for foreign relations.  A local population from a given country tends to influence the country back home to be friendly, and the fact that the country allows its nationals in avoids feelings of the receiving country being selfish, racist, what have you.  As things are now a lot of the hate directed toward the States is because of its restrictive immigration -- the US really is seen as racist and selfish and only interested in exploiting the rest of the world by large numbers of people, for just this reason.

There is a well-known tendency for those who immigrate to be more ambitions, more energetic and more intelligent than those who stay home.  If you look at immigrant populations, such as Asians or Jews or Eastern Europeans, within a generation or so they begin to be at the top of the achievement ladder, so long as they are not held down too much by discrimination (which is what holds down African and Mexican Americans).  In other words, with open immigration a country tends to get the "cream of the crop."

-- A side note here about Latin America -- the US cannot afford to have such a large country as Mexico poor and feeling exploited -- allowing them more freely into the States is almost a necessity, as otherwise you have hate brewing in Mexico and a large illegal population in the States who feel no loyalty and also feel exploited.

New arrivals, especially if uneducated, not speaking English, poor, and so on, are a temporary burden on educational and health care systems (both of which in the States are in huge need  of massive overhaul anyway) and in some limited cases add to crime.  This is short term until they become acculturated, and the investment is worth it.

Businesses in a country with unrestricted immigration can freely recruit what they need anywhere without the need to ship the jobs overseas -- not that they get cheap labor as a competitive labor market quickly nips anything like that -- but that they can find the best skill sets and best track records anywhere without a lot of bureaucracy and difficulty.  This helps the economy.

A growing population naturally brings about a growing economy, and the nation stays strong, with a ready pool of people for the military and the economy.  It also stays younger, with a large pool of working people to support the elderly (with present demographic trends services like Social Security are going to have to be steadily limited more and more so as not to be such a huge drain on the economy).  The birth rate in the States, as with most developed countries, is just not enough to sustain the present population, let alone grow the nation.

Without more people the US will soon become like Britain -- important but not dominant.

As Islam is today, I can see where allowing massive numbers of Muslims in would cause fear -- even though the vast majority would acculturate over a couple generations, such a community would tend to produce a certain number of terrorists and other evils, in spite of their parents.  I can't see any good way to manage that, and admit it.

I can also see some restrictions being reasonable -- a sort of point system without a waiting period -- for education and English and family relations and freedom from criminal record, but not numeric limits or quotas.  (Quotas are inherently racist even if not intended as white countries don't fill their quotas and brown and black countries develop long waiting periods).

One final thing -- what other countries do is beside the point -- that one country is stupid doesn't mean the States has to be stupid too.