What laws apply on the non-inhabited US territories?

Factual Questions
1

Besides the 50 states and 1 federal district, the United States possess 14 (and lay claim to 2 more) insular territories. Of these, 5 are permanently inhabited and have their own governments/laws. But what about the 9 to 11 others? Although not permanently inhabited, persons do find themselves physically present on them at times (e.g. researchers going to Palmyra Atoll). When people are present there, what laws are they subject to?

So if for example, (God forbid) a rape or murder occurred there. Which federal statutes would it be tried under?

Or what about civil law? What if someone, for example, smashed up someone’s car while visiting Palmyra Atoll. Would there be any civil law system they would be subject to? Could we talk of anything like family law existing there? Obviously you couldn’t get married or divorced in these places, but while being there, could you still be deemed to be subject to any rights and duties arising from marital or parent-child relations?

What courts would have competent jurisdiction to try people who had committed a crime or caused damage during a visit to one of these territories? Surely the fact that they are not permanently inhabited doesn’t mean anarchy reigns there?

2

@themapleleaf Funny you should mention Palmyra Atoll, since a murder happened there:

So you sure can get tried and sentenced for murder there.

3

Basically they are all federal government reservations, so federal laws apply (technically automatically in Palmyra as an Incorporated Territory, as determined by Congress in the others).

The ones with permanent bases or stations whatever authority runs that may be delegated by Congress the management of civil affairs, t be referred to the federal court with jurisdiction (e.g. in Wake Island, the General Counsel of the Air Force enforces the Wake Island Code Wikipedia Entry ).