I understood that it would indeed freeze completely - it would just have a different crystalline structure than regular ice that freezes at room temperature. Some of the molecular configurations result in higher density than liquid water, so it would actually contract rather than expand in those instances.

You can try this at home with a bottle of beer. Put it in the freezer, forget about it (happens to me all the time) and open it. It freezes instantly.

I think that is right, since the freezing points / boiling points are also influenced by pressure. So when it tries to expand and cannot expand due to an unbreakable container, the pressure increasing substantially, and the respective points also change.

I'm sure if you try to boil water to steam, and keep it in a container that cannot expand, it won't convert completely to steam, since pressure increases its boiling point. With the conversion to ice, I am not exactly sure (something similar happens possibly) just because it is a little atypical in terms of volumes and liquid / solid states. Also, too tired to look this up :)