Though if it is polarized, it should be three-prong one, to physically prevent connecting it the other way.

But as Germans and their Schuko have shown, it doesn't really matter ;)

US polarized plugs have the neutral pin physically bigger than the line pin. They don't need the third prong to make it one-way, that's only needed for conductive-cased items to have a ground connection.

Nope, the neutral prong is wider on polarized plugs. Nearly all two-prong plugs are polarized, it's just stuff like transformers or soldering irons that aren't.