As an adjective, "US" does not require "the". The reason that, for example, "the US president" requires "the" is because there is one president, not because of the use of "US". That is, we are saying "the president", and adding the extra information of the president being the US president.
For most of your examples, we do not require "the" when used generally, or with another determiner (like a possessive). For example:
This interferes with US interests in the Middle East.
US President Richard Nixon was accused of criminal activity.
The US President held a press conference last Tuesday.
Officials are still debating US foreign policy matters.
There was criticism of several US policies last week.
These are all perfectly natural ways to discuss plural, general, or non-count nouns. Generally, you can replace "US" with "Canadian", and the results will be the same. For example, "This intereferes with Canadian interests in the Middle East." Since you wouldn't use "the" in this example, you shouldn't use it with "US", either.