That’s assuming the 2D representation is representative of near uniform density. In 2D an I-beam and and a solid beam look identical, but they don’t represent the same amount of mass for potential energy minimization.
Play with 3D shapes and you could get identical 2D cross sections to float in arbitrary orientations.
You can but only under very arbitrary situations that aren't common in real life. And if you're assuming it's not hollow and has constant density, then I doubt there's any way to make such an iceberg except if you look at it from one specific angle: looking from the side should give it away. Yet nearly every image of an iceberg seems to show them in that way.
That’s a different question. In practice floating icebergs are often at a local minima not the global minima. They can be at very unstable orientations in calm seas. The constant melting process promotes instability.
Play with 3D shapes and you could get identical 2D cross sections to float in arbitrary orientations.