Premise:
"Anse had subsided, though he was still watching the sergeant with an unrelenting gaze."
Hypothesis: Anse was still watching the sergeant.

yes

Premise:
"The Wall Street Journal says marshmallows are the new rage in fancy restaurants."
Hypothesis: The Wall Street Journal says marshmallows are the new rage in fancy restaurants all across the world.

it is not possible to tell

Premise:
"where the um the military is running around and they're sort of getting restless and a restless military is the kind of thing that happens you know when the Baltic States when they just go in there"
Hypothesis: I restless military happens when they go in there.
yes