Yes, breaking the sound barrier in any medium (including air) will result in a buildup of sound waves (pressure waves) which causes a sonic boom.
However, the high viscosity and higher speed of sound in water means a ridiculous amount of energy will be needed to create that sonic boom.
Absolutely! You'd need insane levels of energy to do so, but you can break the sound barrier underwater, in oil, in a pool of alcohol, etc. The higher the density of the medium, the higher the speed of sound. Even solids objects have a finite speed of sound (but those are stupidly high numbers). So that means when you're in outer space (i.e. a vacuum with zero density) any movement at all means you're breaking the speed of sound - and you're basically at Mach infinity!
Yes. BUT you are breaking a different sound barrier. The speed of sound in different materials is different.
Its much more difficult to do in water, as water is much more difficult to compress. You need to be in a compressible fluid. Liquids are technically compressible fluids, but much LESS compressible than gasses. This is primarily dependent on density.
For clarity, the speed of sound in air is 343 m/s (at sea level atmospheric and room temp), while in water it is about 1500m/s (sea level, room temp)