Some people believe that gravity doesn't exist

[Anomalocaris]

That’s one way to look at it.

Another way is when the submarine is floating, it’s water displacing shape is the usual cigar shaped cylinder that exclude water from its outside.  When it submerges, it’s water displacing shape becomes a complicated thing in which various parts of the interior of cylinder  transforms into pinched off pockets of the exterior water.

So the submarine changed its water displacing shape, even if not its hydrodynamic shape, when it submerges.

No.

Yes.   A submarine submerges by reducing the amount of water it displaces.  It does so by allowing water into parts of its interior, name the ballast tanks, that formerly excluded, thus displaced, water. Thus it now displaces less water.