In general the government has only accepted the idea that refusal to answer questions can't be held against someone in the context of a criminal trial. For example you can certainly take the fifth in a deposition or examination in a civil case, ideally on an attorney's advice, but this decision can be held against you for civil purposes (for instance, the judge can instruct the civil jury that it can consider why the witness didn't want to answer the question). The government's position is most likely that the immigration proceedings have an analogous status where you may be allowed to decline to answer, but an adverse inference can still be drawn from your refusal (like making an assumption that you had something to hide).
Outside of dictatures, people are born with all the rights, and the law is made to remove them. Those law are generally made to protect the rights of other. The main law that doesn't enter this category is immigration law since changing country doesn't remove any freedom to the citizens of the country of arrival.
It's really fun stuff.
The 5th amendment doesn't really apply because entry to the US on a visa isn't a criminal prosecution; no one is compelling you to answer the question, you can choose not to by choosing not to apply for a visa.
In theory, but historically speaking not really: https://scholarship.law.georgetown.edu/cgi/viewcontent.cgi?r...
But then again, it doesn't seem to work very well for US citizens these days either.
As a non-citizen, the internal arguments of the US legal system aren't very interesting to me, but the historical record of how the US treats non-citizens is. The US has clearly demonstrated that in practice, non-citizens are not protected by the same rights.
If you are a non-citizen living here, you'll generally enjoy most of the protections of the constitution and laws. If you are sitting there at customs just visiting, there are a lot of those protections that simply don't apply. Of course, some of those protections don't apply to citizens at these places either, though they play out a bit differently.